Lamar University - ECON 5370

Part B. Solve the following problems.

1)Suppose that the spot exchange rate between the Japanese Yen (Y) and the U.S. dollar ($) was Y110/$1 in 1990. Between 1990 and 1995, the consumer price index rose 20% in Japan, and 30% in the U.S. Then what will be the sport exchange rate in 1995 predicted

by

the Purchasing Power Parity Hypothesis?

2. Diamond Brewery is re-evaluating its optimal combination of inputs (which are imperfect substitutes) as a result of recent union-negotiated wage increases. At the present time, the MP of labor on the production line is 10 cases of beer per hour and the price of a unit of labor service (P_L) is $10/hour. The MP of capital is 12 cases of beer per hour, and the price of a unit of capital's service (P_K) is $8/hour.

1. 1. 1. Employ the least-cost input rule to determine whether the input combination at Diamond Brewery is optimal. Explain why or why not.

1. 1. 2. If the present input combination is not optimal, how can Diamond Brewery reduce

of production for a given output or increase output with a given total cost? (Explain whether and why the company should use more capital and less labor, or less capital and more labor.)

1. 2. Alpha company can produce paintings of equal quality using artists (L) and/or robots (K).

Further, MPs of the artists and the robots are constant such that the two inputs are perfect substitutes in production. The MP of an artist is 40 paintings/day and the price of an artist’s service (P_L) is $20/day. Meanwhile, the MP of a robot is 80 paintings/day and the price of a robot’s service (P_K) is $80/day. To attain optimal input combination (i.e., cost- minimization for a given output or output maximization with a given TC), how should the company employ artists and robots? (Explain why.)

1. 3. Explain whether each of the following production functions exhibits increasing, constant, or decreasing returns to scale. Here, L, K, and M respectively denote labor, capital, and

material

(Proof is required).

a) Q = 3L^0.5K^0.4 +1000L

b) Q = 10K + 5L +1000

c) Q = 10K0.2L0.3M0.6

1. 4. Suppose Zeta company has the following short-run production function, where Q is output per time period and L is the number of units of labor hired. (2 points for each question)

10

Q = -(1/3)L³ + 4L² + 20L

1. 1. 1. What will be L and Q at the maximum short-run output (Q)?

1. 1. 2. What will be L and MP_L at the maximum MP_L?

1. 1. 3. At what level of output will the firm reach the point of diminishing returns to L?

1. 1. 4. Find L, AP_L and MP_L at the maximum AP_L.

1. 1. 5. Determine the boundaries of the three stages of production (i.e., Stage 1, Stage 2, and Stage 3) in terms of L.

1. 5. Suppose a firm has the following total cost function:

TC = 1000 + 240Q - 4Q² + (1/3)Q³

1. Write the equations for:
   1. Average fixed cost:

1. 2. Average variable cost:

1. 3. Marginal cost:

2. Determine the output level and value of MC at which MC is minimized.

3. At what level of output does the diminishing returns set in?

4. Determine the output level, and values of AVC and MC at which AVC is minimized.

1. 6. The following is the relationship between the crew size (L) and the amount of fish caught per day in hundred pounds (TP = Q) for a fishing firm.

L            TP=Q               MP_L            TR             MRP_L             TLC                  MFC_L

0              0                                   $          _                             $                  

1              5          $---------                          $---------                                    $----------

where MRP_L = marginal revenue product of labor, TLC = total labor cost, and MFC_L = marginal factor cost of labor.

1. 1. 1. Assuming that the firm can sell all the fish for $100 per 100 pounds (i.e., P = $100), and can hire as many crew members as the firm wants by paying them $200/day per crew member (i.e., P_L = $200), complete the above table.