# Bus 207 Assignment 3

Reading:

Appendix to Ch. 4: A Calculus Approach to Individual Behavior

Lecture Notes

Hand in the following questions only as part of Assignment 3: Qs 1, 2, 5, 8, 9, 10, 11.

Q1. A firm has decided through regression analysis that its sales (S) are a function of the amount of advertising (measured in units) in two different media, television (x) and magazines (y): S(x, y) = 100 – x2 + 30x – y2 + 40y (a) Find the level of TV and magazine advertising units that maximizes the firm's sales. (b) Suppose that the advertising budget is restricted to 31 units. Determine the level of advertising (in units) that maximizes sales subject to this budget constraint.

(c) Give an economic interpretation for the

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Q9. Ilkka’s income is $120 and he spends it on two goods, X and Y. His utility function is U = XY. Both X and Y sells for $2 per unit.

(a) Calculate Ilkka’s utility-maximizing purchases of X and Y.

(b) How will his utility change if his income decreases by $2.00? (c) If the price of X increased by 44%, with no change in the price of Y, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above? Q10. Suppose a firm produces widgets on two assembly lines and operates with the following Total Cost function: TC = 3x2 + 6y2 – xy

Where x represents the number of widgets produced on one assembly line and y the production on the second. The firm is under contract to produce 20 widgets. (a) Use the Lagrangian method to calculate the least-cost allocation of production to the two assembly lines. (b) What is the firm’s total cost equal to if it fulfils its contract? (c) Give an economic interpretation to the value of the Lagrangian multiplier. (d) Should this firm accept an offer of $60 to produce an additional widget? How about an offer of $80? Explain. Q11. In a particular region, there are two lakes rich in fish. The quantity of fish caught in each lake depends on the number of persons who fish in each according to Q1 = 15 N1- 0.5 N12 and Q2 = 8 N2 - 0.2 N22 where N1 and N2