Topic 7. Variation of the factors of production and their optimum (6 hours)

1. Producer’s behavior. Production function with two variables.

2. Isoquant and Isocost. Marginal rate of technical substitution

3. Cost minimization (Producer’s choice optimisation)

Give the definitions (and if possibly formulas) for the following terms:

Cobb-Douglas production function

Isoquant

Isocost

MRTS

Producer’s optimum

Answer the following question:

1. What are the main characteristics of isoquant?

2. What are the isocost features?

3. What can cause the changes of isoquant (and isocost) position?

4. What is the meaning of Marginal rate of technical substitution?

5. How is it possible to express the producer’s optimal decision?

6. What is the definition and the graph of the firms development curve?

Find the analogous concepts in the theory of the firm.

Consumer theory	Theory of the Firm
Total Utility
Marginal Utility
Utility Function
The law of diminishing marginal utility
Consumption
Indifference curve
Consumer budget
Budget line
MRS
Consumer’s Optimal choice

Solve the problem sets given below.

1. A firm’s production function is Q=5L^0.5*K^0.5, where L- amount of labour hours, К- amount of hours of machinery works. Let us suppose that the firm uses 9 hours of labor and 9 hours of machinery every day. What is the maximum amount product the firm can produce. What is the the maximum amount product the firm can produce if both labor and capital doubled. Calculate the return to scale for this firm.

2. A firm’s production function is given below. Calculate the marginal product of each factor of production:

А) Q=10L⁶K⁵_.

Б) Q=5L^0.5*K^0.5

В) Q(x₁,x₂) = 6x₁ + 17x₂

3. In the figure below the initial isocost (AB) and the new isocost (AC). The firm maximizes the profit and plan to spend 500 000 hrn. to purchase factors of production.

What was initial price of labor, the initial price of capital? Write down the equation for isocosts AB and AC. Calculate the slopes of isocosts. Find out the equilibrium points. What is the value of MRTS in these points?

4. A firm’s production function is Q=(LK)/2 Price of labor is 20 money units Price of kapital is 10 money units. How much labor and capital should use the firm to to produce 400 units of output?

5. A firm’s monthly payment for the equipment is 400 thousand hrn, monthly payment for hiring labor force is 300 thousand hrn. MP_L and MP_K are equal 0,5 and 1. Is it optimal quantity of resources used?

6. МР_L = 100К-L, МР_к=100L – К. What is the maximum potential output of the firm if labor capital expenditure is $1000, Р_к=$5 ., Р_л=$2.