Solved Problems in Consumer Behavior Producer Behavior and Cost

Solved Problems in Consumer Behavior Producer Behavior and Cost

Consumer Behavior

1. Graph the following indifference curves for the given utility levels:

U (x, y) = min {X, Y} for U = 20, 30, 40. (What kind of relationship exists between these goods? Substitutes, Complements?

1. Consider the utility function for a utility maximizing individual consuming two goods X and Y. U (X,Y) = Y² X + (30/2). This person pays 3 dollars for good X and 4 dollars for good Y with an income of 90 dollars. (3 X + 4 Y ≤ 90) Budget constraint.  The marginal utility functions for good x and good y are respectively U_x   = MU_X = Y²  and  U_y   =  MU_Y = 2 X Y
2. Find the marginal rate of substitution between x and y.
3. Find the amounts of good X and Y that maximize this utility.
4. Compute the corresponding utility.

Producer Behavior

1. Suppose the following production function: Q = 10 (K)^1/3 (L)^2/3 subject to:

W *L + r * K = Cost.

8. Suppose that K the amount of capital is K =8. If this company hires 64 workers (L), calculate the value of Q.
9. Determine if this production function exhibits constant, increasing, or decreasing returns to scale.

Costs

1. Consider the following cost and benefit functions:

C(X, Y) = 15 (10 X + 2 X²)   with   MC (X) = 15(10 + 4X)

B(X, Y) = 5 (80 X – 2 X² + 40 Y –  Y² + 2 X Y)  with  MB (X) =  5 (80 – 4 X + 2 Y)

• For Y = 5, derive the benefit and marginal benefit functions (hint: simply replace y by its value, simplify, and you should have the equations).
• Find the value of x at which TB (X) = TC (X) if any
• Find the value of x for which the net benefit is maximized. (MC = MB).
• Calculate the values of the benefit, cost, and net benefit for this value of x.
• Graph the MB and MC functions. You can use any software (preferred) you like, or manual graph, but it must show all important details. (This graph is worth 15 points)

12. Consider the following cost function: TC = 12.5 Q² + 4 Q + 50 MC = 4 + 25 Q
13. Find the fixed cost and the average fixed cost.
14. Find the variable cost and the average variable cost.
15. Find the total cost and the average total cost.
16. Find the output that minimizes the average total cost.
17. Find the output level at which the average variable cost is minimized.