Question 2 a) The supply curve of a product is Q = 10P¹/³. Find the producer surplus when P=8. b) The number of kilograms Q of tomatoes harvested from a field in a day is given by the production function, Q = 150L¹/3. Find the profit maximizing number of people to employ on this farm if each kilogram of tomatoes is sold for 20 cedis, and each worker is paid an average wage of 40 cedis per day. c) A firm is breaking even in a competitive market. Is this firm making zero profits? Explain d) A car wash business washes 11,000 cars per year. The price charged per vehicle washed is 10 cedis. The total cost (total economic cost) of washing these 11000 cars each year is given as 120,000 cedis. Included in this total cost is a fixed cost of 15 percent of the 160,000 cedis capital provided by the financier of this car wash. That is, the financier could have earned 15 percent interest on this capital in the money market if he had not used it to set up this car wash. Is this car wash making profits at the end of the year? Compute the profit. If the firm is not making profits, should it shut down? i. ii. (10

Question 2 a) The supply curve of a product is Q = 10P¹/³. Find the producer surplus when P=8. b) The number of kilograms Q of tomatoes harvested from a field in a day is given by the production function, Q = 150L¹/3. Find the profit maximizing number of people to employ on this farm if each kilogram of tomatoes is sold for 20 cedis, and each worker is paid an average wage of 40 cedis per day. c) A firm is breaking even in a competitive market. Is this firm making zero profits? Explain d) A car wash business washes 11,000 cars per year. The price charged per vehicle washed is 10 cedis. The total cost (total economic cost) of washing these 11000 cars each year is given as 120,000 cedis. Included in this total cost is a fixed cost of 15 percent of the 160,000 cedis capital provided by the financier of this car wash. That is, the financier could have earned 15 percent interest on this capital in the money market if he had not used it to set up this car wash. Is this car wash making profits at the end of the year? Compute the profit. If the firm is not making profits, should it shut down? i. ii. (10

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter18: The Markets For The Factor Of Production

Section: Chapter Questions

Problem 3PA

See similar textbooks

Similar questions

1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…
13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³ K+z! Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.
13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³K+zł Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.
3. A firm has a production function given by 1 1 A) y = 4x³x² ; 1 1 B) y = 3x4x² ; a) What are the factor demand functions? b) What are the conditional factor demand functions? c) What is the cost function? d) What is the supply function? 1 1 C) y = 5x³x2; 11 D) y = 12xx².
2. The market for a slice of pizza in Oakland is highly competitive. The market demand for a slice of pizza can be summarized by the function: D(p) = 1200 — 200p. Consider each pizza shop to be an individual firm with the 1 same cost function C(q) = FC + - q2, where FC represents fixed cost of renting a space from which to sell pizza, and the variable costs reflect the cost of the labor involved in producing and selling pizza. a. In the short-run (e.g. the six months following the signing of a lease for a space from which to sell pizza) determine the quantity each pizza shop would produce for any price in the market. b. In what way does your answer to part (a) depend on the fixed cost? Explain your answer in no more than two sentences. c. Suppose initially there are 100 pizza shops selling pizza in Oakland. Derive an expression for the short-run market supply for pizza. d. Find the short-run equilibrium price and quantity in the Oakland pizza market. How does this equilibrium depend on…
1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y21 + y22, where α is some constant.a) What restriction on α is required to guarantee that this cost function exhibits economies ofscope?b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 andy2.2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:• The market is a perfectly competitive market. Assume there are identical firms with marginalcost of 12 in this perfectly competitive market.• The market is dominated by one monopolist with a marginal cost of 12. This monopolist isable to achieve 1st degree pricing.• The market is dominated by one monopolist with a marginal cost of 12, but the monopolistis able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:(Q∗1 = 30, p∗1 = 35), and (Q∗2 = 60, p∗2 = 20).• The market is dominated by one monopolist…
Consider a competitive market for red lentils with 100 identical farmers in Horsham Victoria, a competitive market price of $5 and the following MC for each farmer: MC = $0.05Q Also consider the following market demand function: QD a) Calculate the optimal level of production (in tonnes) for each farmer (show workings) = = 1000 - 40P b) Assuming 100 lentil farmers of equal size how many tonnes of lentils in total will be supplied in the entire market? (show all workings) c) Consider that the government now imposes a 25% tax on producers, calculate i) the new equilibrium level of output for each firm (hint - think about how this affects each farmer's marginal cost), and ii) new total supply in the entire market (show all workings)
1.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5x + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p.
3. Suppose the production function of a firm is given by f (x1, x2) = min {x1, x2}. (a) Calculate the conditional demand functions of the firm assuming w₁ = 2, w2 = 4, and y = 8. (b) Calculate the minimum cost of the firm to produce 8 units of the good when w₁ = 2 and w2 = 4.
7. Assume that the marginal cost curve is given by mc(q) = 100 + 2q. (a) If the price is $160, what is the optimal production for the firm? What if the price is $120? (ignore the shut-down decision for this part) (b) Assuming that the market is cleared at $160 (no shortage/surplus). If the market demand is equal to 10,000 units of the product. How many firms are currently operating (n) in the market? (Hint: if the market clears qª = n x q°) (c) If the total cost curve is TC 256 + 100g + q², what's the average total cost curve? %3| what's the break-even price? (d) If the demand curve is given by qd = 8, 452 – p, what's the long-run equilibrium price, the equilibrium quantity and the long-run total number of firms (n) in the industry?
Suppose that the market for dress shirts is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. (?) 50 45 40 35 30 ATC 25 20 15 AVC 10 MC 5 + 2 4 6. 8 10 12 14 16 18 20 QUANTITY (Thousands of shirts) For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down, it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.) Price Quantity Total Revenue Fixed Cost Variable Cost Profit (Dollars per shirt) (Shirts) (Dollars) (Dollars) (Dollars) (Dollars) 12.50 7,500 135,000 27.50 135,000 45.00 135,000 If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's fixed cost is…
2. Suppose the production function of a firm is given by f (x₁, x2) = 2x₁ +4x2. (a) Calculate the conditional demand functions of the firm assuming w₁ = 2, W₂ = 3, and y = 8. (b) Calculate the minimum cost of the firm to produce 8 units of the good when w₁ = 2 and w2 = 3.