Question

1. Production costs are constant along an isoquant.
a. True
b. False

2. A map of isoquants provides a full description of the technology used by a producer.
a. True
b. False

3. Changing labels on the isoquants without changing the shapes of the isoquants implies no change in the underlying technology as long as the ordering of isoquants is preserved.
a. True
b. False

4. Suppose that at a given input combination the marginal product of labour is 8 and the marginal
product of capital is 2. What is the TRS at that input combination? (Note: Unless otherwise stated, in
this subject the TRS is the technical rate of substitution of labour with respect to capital, i.e. the TRS is the slope of the isoquant at a given input combination when the isoquant is represented in a
graph with labour on the horizontal axis and capital on the vertical axis.)
a. -1/4
b. -16
c. -4
d. None of these

8. Decreasing returns to scale implies increasing marginal costs of production.
a. True
b. False

9. Increasing returns to scale implies decreasing total cost of production.
a. True
b. False

10. If the marginal cost of production is lower than the average cost, then it must be that the
average cost is decreasing.
a. True
b. False

11. Suppose the input combination currently used by a producer is such that the TRS is equal (in
absolute value) to the ratio of the input prices. Then, we can conclude that the producer is
maximizing her profits.
a. True
b. False

12. Consider a production technology in which two inputs are perfect substitutes. Any producer
using this technology who wishes to minimize the production cost will use only the cheaper of the
two inputs.
a. True
b. False

14. Suppose the technology of a producer is described by the production function ?? = min{ℓ, 4??}. If the price of labour is w=$1 and the price of capital is r=$2, what is the cost of producing 20 units of
output?

15. Suppose labour and capital are perfect complements in production. More precisely, suppose the
production function is ?? = min{ℓ, 2??}. Suppose the producer is currently facing a price
of labour w=$1, and she is currently using bundle (ℓ, ??) = (4,2), which allows her to produce 4 units
of output. What is the increase in the cost of producing 4 units of output if w increases to $2 (and
the price of capital remains unchanged)?

16. Suppose you are told that the cost function of a given producer is given by C(w,r,x)=wrx2
. (In this
case, MC(x)=2wrx.) Then you can conclude that the technology of that producer is characterized by:
a. constant returns to scale
b. decreasing returns to scale
c. Increasing returns to scale
d. There is not enough information to answer

17. Suppose you know that the cost function is C(w,r,x)=wrx2 and w=r=$2. Then you can conclude
that the lowest cost of producing 3 units of output is $40.
a. True
b. False because we can conclude that the lowest cost of producing 3 units is not $40
c. False because we would need to know the TRS to find the lowest cost of producing 3
units
d. False because we would need to know the output price to find the lowest cost of
producing 3 units

18. Suppose the marginal cost and the average cost of production are given by the following
expressions: MC(x)=3x1/2 and AC(x)=2x1/2. What is the profit maximizing quantity when p=$6?

19. Suppose the marginal cost and the average cost of production are given by the following
expressions: MC(x)=3x1/2 and AC(x)=2x1/2. What is the value of the long-run break-even price?

Answer 1

Answer 1. False as isoquants only reflect the combination of inputs used in production to produce same level of output. Isoquants do not reflect same production costs. Same production costs are reflected by isocost lines.

Answer 2. True an isoquant map provides description about technology used by a producer. In some cases producer use two inputs together which generate a kink shape isoquants , some inputs are used as perfect substitutes by producer which generate downward sloping straight isoquants, isoquant also reflects technology used as imperfect substitutes (convex). Overall an isoquant map describes technically efficient combination of resources that can produce different levels of output.

Answer 3. False as changing labels on isoquant means every isoquant will produce some different level output and to achieve that level of output, technology and combination of inputs will be changed by producers.

Answer 4. Given that marginal product of labor is 8 and marginal product of capital is 2 . TRS ( technical rate of substitution) is given by dividing marginal product of labor by marginal product of capital i.e.

Minus sign indicate the decrease in capital to increase labor by 1 unit to produce some given level of output on an isoquant.