# Solved Problems in Consumer Behavior Producer Behavior and Cost

Solved Problems in Consumer Behavior Producer Behavior and Cost

Consumer Behavior

- 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?

- Consider the utility function for a utility maximizing individual consuming two goods X and Y. U (X,Y) = Y
^{2}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}= Y^{2}and U_{y }= MU_{Y}= 2 X Y - Find the marginal rate of substitution between x and y.
- Find the amounts of good X and Y that maximize this utility.
- Compute the corresponding utility.

Producer Behavior

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

W *L + r * K = Cost.

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

Costs

- Consider the following cost and benefit functions:

C(X, Y) = 15 (10 X + 2 X^{2}) with MC (X) = 15(10 + 4X)

B(X, Y) = 5 (80 X – 2 X^{2} + 40 Y – Y^{2} + 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)

- Consider the following cost function: TC = 12.5 Q
^{2}+ 4 Q + 50 MC = 4 + 25 Q - Find the fixed cost and the average fixed cost.
- Find the variable cost and the average variable cost.
- Find the total cost and the average total cost.
- Find the output that minimizes the average total cost.
- Find the output level at which the average variable cost is minimized.

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