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Homework answers / question archive / University of Pittsburgh Fall 2014 Intermediate Microeconomics Second Exam 1)Suppose the total cost of producing T-Shirts can be represented as TC = 50 + 2q

University of Pittsburgh Fall 2014 Intermediate Microeconomics Second Exam 1)Suppose the total cost of producing T-Shirts can be represented as TC = 50 + 2q

Economics

University of Pittsburgh

Fall 2014

Intermediate Microeconomics Second Exam

1)Suppose the total cost of producing T-Shirts can be represented as TC = 50 + 2q. Which of the following statements is True at all levels of production?

A. MC = AV C B. MC = AC

      1. MC > AFC
      2. All of the above E. None of the above
  2. When the isocost line is tangent to the isoquant, then
      1. MPL = MPK
      2. the firm has achieved the right economies of scale
      3. the firm is producing that level of output at minimum cost.
      4. All of the above E. None of the above
  3. Suppose MPL = 0.5·(q/L) and MPK = 0.5·(q/K). In the long run the firm will hire equal amounts of capital and labor
      1. all of the time
      2. only when w=r
      3. only when 2 = 0.5 · r
      4. at no point in time
  4. An orange grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x1,x2}, where x1 and x2 are the amounts of inputs 1 and 2 that she uses. The prices of these two inputs are w1 = $8 and w2 = $3, respectively. The minimum cost of producing 140 units is therefore
      1. $280
      2. $630
      3. $770
      4. $980
      5. $1,330
      6. None of the above.
  5. Ann wants to go into the donut business. For $500 per month she can rent a bakery complete with all the equipment she needs to make a dozen different kinds of donuts (K = 1,r = 500). She must pay unionized donut bakers a monthly salary of $400 each. She projects her monthly production function to be Q = 5LK where Q is tons of donuts.
    1. With the current level of capital, what is the marginal product of labor? is the marginal product diminishing? Explain.
    2. If Ann wishes to make 25 tons of donuts, how many bakers are required given the current level of capital?
    3. Derive Ann’s short run cost function with K = 1. How much will it cost to produce these 25 tons of donuts (total cost)?
    4. Derive the marginal cost curve from your answer to (c) and show the relationship between the marginal cost and the marginal product of labor. In other words, express marginal cost and marginal product of labor as equations and compare the two in order to determine the relationship at the optimum.

 

    1. Now suppose Ann is in a long run scenario. How much labor and capital will she optimally employ to produce 25 tons of donuts? This is a continuation of question #5
    2. Continue to suppose Ann is in a long run scenario. How much will it cost Ann to produce 25 tons of donuts? This is a continuation of question #5
    3. Carefully explain any differences between your answers to (c) and to ( f ). This is a continuation of question #5

 

  1. A firm wishes to produced Q = 30 as cheaply as possible using only labor (L) and capital (K) with a relationship explained by the following production technology: Q = L+2K. The prevailing market wage is $5/hr. You will need to work carefully to determine the rental rate of capital, r, as specified by the items below:
    1. Find r so that the firm can optimally employ 10 workers and 10 machines

 

to produce output: Q = 30 while still minimizing costs. Show all work to report r and the total minimum cost associated with this level of production.

 

Then cost is minimized with any combination of L and K sufficient to produce Q = 30. Here we have: 5(10) + 10(10) = 150.

    1. Suppose it currently costs the firm $150 to produce Q = 30 units of output optimally. Identify the greatest lower bound for the rental rate of capital, r. In other words, what is the smallest possible price to use capital that this firm could be facing, given the information provided?
    2. Now suppose the rental rate of capital drops i.e. r falls to be strictly less than the bound you identified in (a). Find the least upper bound on the minimum

 

cost to produce Q = 30. In other words, find the largest amount that the cost

 

minimizing firm would be paying to produce Q = 30 assuming it is still optimizing after the reduction in r.

 

                                                         

 

 

  1. Rippin’ Good Cookies is based in Ripon, WI. Fun Fact: In addition to free cookie samples this small town is also famous as a claimant to the title of ‘Birthplace of the Republican Party’. Suppose the cookie factory uses two inputs to produce cookies according to a

√

production function given by f(x1,x2) = 2 x1+x2. Cookies sell at $50 per crate. Input 1 costs $5 per unit and input 2 costs $50.

    1. If input 2 is fixed at x2 = 10, find the profit maximizing level of x1.
    2. What profit level, associated with your answer to (a), is enjoyed by Rippin’ Good Cookies when x2 = 10 ?
    3. Suppose Rippin’ Good Cookies is free to vary its usage of all inputs. What is the profit maximizing level of x1?
    4. Suppose Rippin’ Good Cookies is free to vary its usage of all inputs. Does the firm need to change its usage of x2 to maximize profit? Explain your answer by writing down a mathematical relationship using p and w2 to characterize the effect of varying x2 on the firm’s profits.
  2. A firm has two plants, one in the United States and one in Mexico, and it cannot change the size of the plants or the amount of capital equipment. The wage in Mexico is $5. The wage in the US is $20. Given current employment, the marginal product of the last worker in Mexico is 100 and the marginal product of the last worker in the US is 500.
    1. Is the firm maximizing output relative to its labor cost? Show how you know.
    2. If it is not, what should the firm do?
  3. Extra Credit. Consider a price taking firm i.e. operating where

P = MR [not a typo] wherein the market price is $25 per unit. Suppose further that the firm’s costs are given by Total Cost = 0.25q2 + 10q + 250, where q is the number of units produced.

      1. Find the firm’s fixed costs, variable costs, marginal costs, average fixed costs, and average variable costs.
      2. What quantity should the firm choose in order to maximize profits in the short run?
      3. What quantity should the firm choose in order to maximize profits in the long run?

 

 

 

 

 

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