Instructions: Please Read Carefully
Please print out this form. There should be four separate sheets of paper (including the cover
sheet). After you have written your answers, please staple the four sheets together at the top lefthand corner.
The first sheet is intended only as a cover sheet. Do not write anything on the first sheet except your
name and ID #.
Please answer each question on the page provided. If you need extra space, you may use the back
of the sheet.
There are 50 possible points on this homework assignment. You may work together, but you
MUST WRITE UP YOUR OWN WORK and TURN IT IN, IN PERSON, AT THE BEGINNING
OF CLASS on Friday, March 22nd. Late homework will not be accepted.

PLEASE STAPLE YOUR
HOMEWORK!!

1. (20 points) Suppose honey is produced in a beehive using bees and sugar. Each honey producer uses
one beehive which she rents for $20/month. Producing q gallons of honey in one month requires
spending 5q dollars bees, and 4q2 dollars on sugar.
a) (5 points) What is the total cost of producing q units of honey for an individual honey producer in a
given month?

b) (5 points) In general, if the total cost of producing honey is a + bq + cq 2, then the marginal cost of
producing honey is b + 2cq. Assuming each honey producer operates as a price-taker, what is the
monthly supply curve for an individual producer?

c) (5 points) Let Q be the total market supply, and q is the supply of an individual firm. Therefore, q =
Q/n where n is the total number of firms in the market. Suppose the demand for honey is given by Q =
512-4P. Also, suppose there are 50 honey producers in the market. What is the equilibrium price of
honey?

d) (5 points) How much profit does an individual producer make in a month? Is this a long-run
equilibrium? If the answer is yes, simply state that it is a long-run equilibrium. If the answer is no,
explain whether or not the equilibrium price will rise or fall.

2. (21 total points) Suppose a firms production function is given by Q = L 1/2*K1/2. This means that
MPL =

K 1/ 2
L1 / 2
, and MPK =
.
2 L1 / 2
2K 1/ 2

Suppose the price of labor is w = 36, and the price of capital is r = 64.
a) (9 points) Derive the firms Total Cost function, TC(Q). Be sure to show your work!

b) (12 points) For this problem, you will sketch the graph of the firms isoquant for Q = 12 units of
output, and on the same graph sketch the firms isocost line associated with the total cost of producing Q
= 12 units of output. To get this total cost, you must use the Total Cost function from part a). Please
scale your graph up to 36 units of Labor on the horizontal axis, and 36 units of Capital on the vertical axis
(do not go above 36 units on either axis). For the isocost line, clearly identify the vertical and horizontal
intercepts. For the isoquant, clearly identify 4 combinations of Labor and Capital that will produce Q =
12 (including the bundle that minimizes the firms cost of production). Make sure your graph is neatly
and accurately drawn and carefully labeled.

3) (9 total points) Suppose there are n identical firms in a market. Each firm has fixed cost equal to 392,
and variable cost given by VC = 2q2, where q is the amount that an individual firm produces. This means
that an individual firms marginal cost is given by MC = 4q. Also, the market demand is given by
P = 1148 3Q, where Q is the total amount of the good produced by all of the firms combined.
Therefore, Q = n*q.
a) How much output will each of them produce?

b) What will be the market price?

c) How many firms will there be in long run equilibrium?



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Your email address will not be published. Required fields are marked *

Instructions: Please Read Carefully
Please print out this form. There should be four separate sheets of paper (including the cover
sheet). After you have written your answers, please staple the four sheets together at the top lefthand corner.
The first sheet is intended only as a cover sheet. Do not write anything on the first sheet except your
name and ID #.
Please answer each question on the page provided. If you need extra space, you may use the back
of the sheet.
There are 50 possible points on this homework assignment. You may work together, but you
MUST WRITE UP YOUR OWN WORK and TURN IT IN, IN PERSON, AT THE BEGINNING
OF CLASS on Friday, March 22nd. Late homework will not be accepted.

PLEASE STAPLE YOUR
HOMEWORK!!

1. (20 points) Suppose honey is produced in a beehive using bees and sugar. Each honey producer uses
one beehive which she rents for $20/month. Producing q gallons of honey in one month requires
spending 5q dollars bees, and 4q2 dollars on sugar.
a) (5 points) What is the total cost of producing q units of honey for an individual honey producer in a
given month?

b) (5 points) In general, if the total cost of producing honey is a + bq + cq 2, then the marginal cost of
producing honey is b + 2cq. Assuming each honey producer operates as a price-taker, what is the
monthly supply curve for an individual producer?

c) (5 points) Let Q be the total market supply, and q is the supply of an individual firm. Therefore, q =
Q/n where n is the total number of firms in the market. Suppose the demand for honey is given by Q =
512-4P. Also, suppose there are 50 honey producers in the market. What is the equilibrium price of
honey?

d) (5 points) How much profit does an individual producer make in a month? Is this a long-run
equilibrium? If the answer is yes, simply state that it is a long-run equilibrium. If the answer is no,
explain whether or not the equilibrium price will rise or fall.

2. (21 total points) Suppose a firms production function is given by Q = L 1/2*K1/2. This means that
MPL =

K 1/ 2
L1 / 2
, and MPK =
.
2 L1 / 2
2K 1/ 2

Suppose the price of labor is w = 36, and the price of capital is r = 64.
a) (9 points) Derive the firms Total Cost function, TC(Q). Be sure to show your work!

b) (12 points) For this problem, you will sketch the graph of the firms isoquant for Q = 12 units of
output, and on the same graph sketch the firms isocost line associated with the total cost of producing Q
= 12 units of output. To get this total cost, you must use the Total Cost function from part a). Please
scale your graph up to 36 units of Labor on the horizontal axis, and 36 units of Capital on the vertical axis
(do not go above 36 units on either axis). For the isocost line, clearly identify the vertical and horizontal
intercepts. For the isoquant, clearly identify 4 combinations of Labor and Capital that will produce Q =
12 (including the bundle that minimizes the firms cost of production). Make sure your graph is neatly
and accurately drawn and carefully labeled.

3) (9 total points) Suppose there are n identical firms in a market. Each firm has fixed cost equal to 392,
and variable cost given by VC = 2q2, where q is the amount that an individual firm produces. This means
that an individual firms marginal cost is given by MC = 4q. Also, the market demand is given by
P = 1148 3Q, where Q is the total amount of the good produced by all of the firms combined.
Therefore, Q = n*q.
a) How much output will each of them produce?

b) What will be the market price?

c) How many firms will there be in long run equilibrium?



Leave a Reply

Your email address will not be published. Required fields are marked *