Microeconomics   (Midterm)

1. Examine whether the following questions are true or false? Explain your answer: 

a) The production function shows the least cost method of producing a given level of output.

b) When marginal product of labor is the same for each unit of labor, the average product of labor is always less than the marginal product of labor.

c) When the income-consumption curve has a positive slope throughout its entire length, we can conclude that both goods are inferior. 

d) The following sentence describe the Giffen good case: When the price of good falls, the income effect is in the opposite direction of substitution effect and consumption rises.

e) The marginal rate of technical substitution is equal to the ratio of the marginal products of the inputs.

f) The average total cost of a given level of output is the slope of the line that is tangent to the total cost curve at the level of output.

2. Suppose a consumer allocates his given income between the commodity X and Y.

a) Derive the price consumption curve through price changes for commodity X on graph and explain.

b) Derive the demand curve of the consumer for commodity X on graph and explain.

3. Explain the relationship between short run and long run costs where there is constant returns to scale by using graph.

4. Let Q be the production function such that Q=K^0.5L^0.5, where K is capital and L is labor. The price of K is 8TL and  the price of L is 2 TL.

a) Does the production function exhibit constant, increasing or decreasing returns to scale?

b) What is the average product of labor?

c) Does capital obey the law of diminishing returns?

d) Suppose the owner of the firm wants to produce 144 units, how much capital and labor should be employed to minimize cost and and what is the cost of production?

e) Suppose the same question as in part d, except the firm has a fixed amount of capital, K=16 now. How much L should be employed to minimize cost and and what is the total cost?