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- 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…VI. | Suppose the cost of producing milkshakes is C = Q³/3-30² +150 +50. What is the equation for marginal cost? At what point is marginal cost minimized?Assume the demand and total cost functions for soccer balls are given in the following form: Demand: P = 120 - 20 and Total Cost: TC = 10Q + Q4. where Q is quantity and Pis the price measured in dollars. a) How many soccer balls is produced in the competitive market? What will be the price in the competitive market? b) Calculate CS, PS and DWL in the competitive market. Show them on a qraph;
- b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)The data below shows tabulation on the production of a hypothetical product.Output (Q) Total cost (TC)Units Kshs.0 - 251 - 322 - 383 - 424 - 485 - 586 - 677 - 788 - 98i. Using the above data, determine:· Total fixed cost · Average variable cost schedule · Marginal cost schedule Suppose this product is produced on a perfect market and the price of the commodity = 10, determine the output Q that will maximize the profits. What is the maximum profits achieved by the firm?6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
- What is relationship between total revenue (TR) and total variable cost (VC) if the price is equal to the AVC (tangent to the minimum AVC), (is TR greater, less, or equal to VC)? What do we call this point?1. The total cost of producing a quantity q is C(q). The average cost a(q) is given in figure below. The following rule is used by economists to determine the marginal cost C'(q0), for any qo: Construct the tangent line ti to a(q) at qo. Let t, be the line with the same vertical intercept as t, but with twice the slope of t, . Then C'(q0), is the vertical distance shown in figure below. Explain why this rule works. $/unit a(q) t2 t1 C'(qo)1. If the cost function of producing a commodity is: 40 + 50x + Vx2 +1 10 C (x) = = where x represents the number of units produced. Calculate the marginal cost of producing 20 units.
- Find the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!Suppose there is a decrease in the demand for high-definition televisions. What effect might this change have on the short-run average total cost curve for this product? _____ a) A decrease. When demand decreases, the short-run average total cost falls. b) An increase. When demand decreases, the short-run average total cost increases. c) No change. Demand determines the final price but not the costs for the product.The marginal revenue (in thousands of dollars) from the sale of x MP3 players is given by R'(x) = 4x(x^2 + 27,000)^-2/3 how many players much be sold for a revenue of at least $40,000?