Question

5) The above diagram shows the market for oranges given current market supply and demand conditions. The government passes the law declaring current equilibrium price to be the “fair” price, and legally imposing “price ceiling” on the price of oranges. Next, suppose that the only change is that demand for oranges goes up. Such change in market conditions would lead to ________ equilibrium price and _______excess demand. Finally, quantity transacted in this market will________. A) lower; no; increase. B) higher; positive; increase. C) higher; no; decrease. D) higher; positive; remain unchanged. E) lower; no; remain unchanged.

6) Suppose that in the above diagram the price ceiling is $7. Note that in the above diagram both supply and demand curves are straight lines. In this case, the consumer surplus is equal to ____ , the producers’ surplus is equal to ______ . A) 200; 40 B) 80; 40 C) 120; 40 D) 120; 80 E) 200; 80

7) Suppose the production function for good q is given by � = � ∙ � where K and L are capital and labor inputs. Consider three statements about this function: I. The function exhibits constant returns to scale II. The function exhibits diminishing marginal productivities to all inputs III. The function has a constant marginal rate of technical substitution Which of these statements are true? A) All of them B) None of them C) I and II but not III D) I and III but not II E) II and III but not I

Answer 1

Answer :

5. D

Explanation: When demand goes up, everything remaining constant, the equilibrium price will go up. However, due to the government imposed price ceiling, the market price does not grow up. As a result, the supply remains the same as suppliers would not supply extra if the price does not go up. So, there will be excess demand and quantity transacted will remain unchanged at the old level.

6.

A) $200; $40

Remember that consumer surplus is area above price line and below demand curve. therefore, consumer surplus

= (1/2)(40)(14 - 10) + {(4)*(10-7)] = $200

and producer surplus is area below price line and above supply curve

= (1/2)(40)(7-5) = $40

7. None of them are correct. Option(B) is correct

q= K.L

Now, to see whether this production function exhibits constant returns to scale. Double the inputs K and L.

By doubling the input we get,

(2K).(2L)

= 2²(K.L)

= 4q >2q [So, this production function exhibits increasing returns to scale

Now, next to see whether this production function exhibits diminishing marginal prductivities to all inputs. Find the marginal product of labor and marginal product of capital.

MP_L = K and MP_K = L

Now, do the second-order partial derivatives of the production function, we get.

d MP_L/dL =0 and dMP_K/dK =0.

This implies that production function exhibits constant marginal productivities to all inputs.

Now, to check whether the production function has a constant marginal rate of technical substitution. Now, calculate the marginal rate of technical substitution.

Marginal rate of technical substitution (MRTS) = MP_L/MP_K = K/L

Now, when we do the derviative of MRTS w.r.t L then, we get the negative value. So, this implies that the production function has a diminishing marginal rate of technical substitution.