ECON 11A Study Guide - Midterm Guide: Root Mean Square, Production Function
econ 11aReview Questions 7 ams 11a
Applied Optimization
Comment: In every problem that you claim to find the absolute
minimum or maximum value of the function in question, you must
justify this claim.
1. Farmer Jones wants to build a 4800 square foot rectangular enclosure for her
vegetable garden. The enclosure will be surrounded by grade A fencing that costs
$12.00 per linear foot, and the interior of the enclosure will be subdivided into
5 equal parts using grade B fencing that costs $8.00 per linear foot, (see Figure
1 below). What should the dimensions of the enclosure be to minimize the total
cost of the fencing? What will the minimal cost be?
Figure 1: Farmer Jones’ vegetable garden.
2. The demand equation for a monopolistic firm’s product is 4p+q= 320, and
the firm’s cost function is given by c= 0.1q2+ 10q+ 1500. Find the price that
maximizes the firm’s profit. What is the firm’s profit?
3. The government imposes a $2.80 per-unit tax on the firm in problem 2. Assuming
that the firm acts to maximize its profit...
(a) By how much will the firm increase the price of its product in response to
the tax?
(b) What is the effect of this tax on the firm’s maximum profit?
(c) What will the government’s tax revenue from the firm be?
(d) How much of this tax revenue will be paid for by consumers?
4. The production function for a firm is given by q= 10k1/4l3/4, where qis the firm’s
output, kis the capital input and lis the firm’s labor input. The price per unit
of capital is pk= $1000.00 and the price per unit of labor is pl= $1250.00.
(a) Find the levels of capital and labor input that maximize the firm’s output,
given that the firm’s total production budget is B= $100000. What is the
firm’s output?
(b) Find the levels of capital and labor input that minimize the cost of producing
2500 units. What is the cost?
(c) What is the (minimum) cost of producing qunits, as a function of q?
5. A (different) firm’s cost function is given by c= 0.02q2+ 20q+ 800. Find the level
of output that minimizes the firm’s average cost.
Document Summary
The enclosure will be surrounded by grade a fencing that costs. . 00 per linear foot, and the interior of the enclosure will be subdivided into. 5 equal parts using grade b fencing that costs . 00 per linear foot, (see figure. Figure 1: farmer jones" vegetable garden: the demand equation for a monopolistic rm"s product is 4p + q = 320, and the rm"s cost function is given by c = 0. 1q2 + 10q + 1500. Find the price that maximizes the rm"s pro t. What is the rm"s pro t: the government imposes a . 80 per-unit tax on the rm in problem 2. Rm"s output? (b) find the levels of capital and labor input that minimize the cost of producing. What is the cost? (c) what is the (minimum) cost of producing q units, as a function of q: a (di erent) rm"s cost function is given by c = 0. 02q2 + 20q + 800.
