Question

1. If U(x,y) = X²Y²
   1. Marginal utility of x diminishes as x increases with y held constant;
   2. Utility increases by two for every one unit increase in the quantities of both x and y
   3. Utility increases by a factor of 2 if x and y are both doubled.
   4. The individual will consume equal quantities of X and Y regardless of their prices.
   5. None of the above.

2. If the production function for good X is X = K^.3L^.5
   1. Long run marginal cost will increase as X increases
   2. Long run marginal cost will decrease as X increases
   3. Long run marginal cost will be the same for every value of X
   4. Long run average cost will be increasing.
   5. None of the above.

3. If the production function for good X is X = K²L^.5
   1. Long run marginal cost will increase as X increases
   2. Long run marginal cost will decrease as X increases
   3. Long run marginal cost will be the same for every value of X
   4. Long run average cost will be decreasing.
   5. None of the above.

4. If the production function for good X is X = K^.5L^.5
   1. Long run marginal cost will increase as X increases
   2. Long run marginal cost will decrease as X increases
   3. Long run marginal cost will be the same for every value of X
   4. Long run average cost will be decreasing.
   5. None of the above.

5.   In the short run at quantity of output 100, total cost is $25,000 and total fixed cost is $10,000.
   1. Average fixed cost at any quantity less than 100 will be greater than $100;
   2. Average variable cost at quantity equal to 100 will be $150
   3. Average total cost will be $100 at quantity equal to 100
   4. If price in a competitive market is $50 per unit, the firm will shut down temporarily.
   5. None of the above.

Answer 1

(1) (e)

Coefficient of both goods is higher than 1. So there is increasing marginal utility and increasing returns to scale.

(2) (d)

Sum of Coefficient of both inputs is less than 1. So, there are decreasing returns to scale, meaning diseconomies of scale. LRATC curve is upward rising.

(3) (d)

Sum of Coefficient of both inputs is higher than 1. So, there are increasing returns to scale, meaning economies of scale. LRATC curve is downward falling.

(4) (c)

Sum of Coefficient of both inputs is equal to 1. So, there are constant returns to scale. LRATC and MRMC curves are horizontal.

(5) (a)

AFC = TFC/Q

When Q = 100, AFC = 10,000/100 = 100

So when Q < 100, AFC > 100.