A firm produces its output using the following production function: 1 f(x1, x₂) = x₁x₂ where x₁ is the amount of input 1 and x2 is the amount of input 2.

Suppose a firm has the following production function  Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8  = (16/Q)+ 4√?  (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.

14. The research department of Acme, Inc. has determined the marginal cost function for one particular item to be m(x) = 0.12e0.04x dollars per item, where x is the number of items produced. If Acme's fixed costs amount to $3,000, find the cost function, C(x), for the company.

Suppose a firm’s cost function is given by: C= 50 + 4q2 a) Find the equations for AFC, AVC and MC. b) If w=$4, what’s the short run production function for this firm?

When a firm produces one unit, the variable cost is $3. When the firm produces two units, the variable cost is $6. What is the marginal cost associated with two units of production.

Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?

A5

K A cereal factory has weekly fixed costs of $22,000. It costs $1.26 to produce each box of cereal. A box of cereal sells for $4.06. Find the rule of the cost function c(x) that gives the total weekly cost of producing x boxes of cereal. OA. c(x)=1.26x OB. c(x)=22,000+ 1.26x OC. c(x)=22,000 +4.06x OD. c(x)=22,000+ 2.8x

A farm produces rice, which is sold in 50 kilogram bags. Let Q denote the number of bagsproduced per week during harvest time. Costs C are denoted in units of dollars. The totalweekly cost function for producing the product is C = 4Q + 100. The total weekly income function for this product is I = 50Q – 2Q2. What is the profit function P as a function of Q and sketch it using P values 0, 5, 10,15, 20 and 25.

1. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.