Microeconomics Answers

1List the properties of homothetic and linearly homogeneous production function

1. The utility function for an individual is given by the equation: 𝑈 = 𝑋1 0.25𝑋2 0.75 and their budget constraint is 𝑃1𝑋1 + 𝑃2𝑋2 = 𝑀 (i) Using the Lagrange, and showing all work, Derive the demand functions for good 𝑋1 𝑎𝑛𝑑 𝑔𝑜𝑜𝑑 𝑋2 (ii) Given that the price for good 1, p1= k2.5 and the price for good 2, p2=k5, and the consumer’s income is k100. Calculate and graphically present the optimal choice for good 1 and good 2. (iii) Calculate the optimal level of utility for the consumer derived from the above optimal bundle. (iv) Show (by calculating) that at a consumer’s optimal point, the slope of the indifference curve equals the slope of the budget line. (v) Suppose government needs to raise revenue through imposing a quantity tax of 0.5 kwacha per unit of good

1. The utility function for an individual is given by the equation: 𝑈 = 𝑋1 0.25𝑋2 0.75 and their budget constraint is 𝑃1𝑋1 + 𝑃2𝑋2 = 𝑀 (i) Using the Lagrange, and showing all work, Derive the demand functions for good 𝑋1 𝑎𝑛𝑑 𝑔𝑜𝑜𝑑 𝑋2 (ii) Given that the price for good 1, p1= k2.5 and the price for good 2, p2=k5, and the consumer’s income is k100. Calculate and graphically present the optimal choice for good 1 and good 2

Goodyear Tire and Rubber Company provided China with the materials and training needed to establish a printing

plant in exchange for finished labels that Goodyear attaches to its tires. What is this an example of?

A market has a demand function given by the equation Qd= 180- 2p and a supply function given by the equation Qs= -15 + p. The market is government-regulated with price support per unit and production quotas.

a. If the price is set at $72 per unit, what production quota is needed to make sure there are no shortages or surpluses.

Explain and show graphically, what happens to the equilibrium price and quantity if a flood destroys much of the water melon crop in Belize and, at the same time, consumer tastes shift toward water melon juice. What would we expect to happen to the equilibrium price and quantity in the market for water melon juice?

4. The following problem traces the relationship between firm decisions, market supply, and market equilibrium in a perfectly competitive market. a. Complete the following table for a single firm in the short run.
output| tfc| tvc | tc | Avc | Atc | Mc |
 0      $150  $0   150  -      -    -
1       150   40   190  40    190   40
2       150   100  250  50    125   60
3       150   180  330  60    110   80
4       150   280  430  70    107.5  100
5       150   400  550  80    110   120
6       150   560  710  93.33 118.33  160
7       150   760  910 108.57 130     200
8       150   1000 1150 125   143.75  240
9       150   1300 1450 144.44 161.11 300
10      150   1850 2000 185    200    550
b. Using the information in the table, fill in the following supply schedule for this individual firm under perfect competition and indicate profit (positive or negative) at each output level. (Hint: At each hypothetical price, what is the MR of producing 1 more unit of output? Combine this with the MC of another unit to figure out the quantity supplied.)
PRICE |QUANTITYSUPPLIED| PROFIT
 $ 40        __         ____ 
   70        __         ____
   110       __         ____ 
   140       __         ____ 
   180       __         ____ 
   220       __         ____ 
   260       __         ____ 
   400

1.    Mike, Rosie, and Shobber live in separate houses along a dark and windy road. The following represent their marginal benefits for street lights:

MB_Mike=200-2Q_M

MB_Rosie=100-Q_R

MB_Shobber=100-2Q_S

where Q_M represents the quantity of street lights consumed by Mike, Q_R is the quantity of street lights consumed by Rosie and Q_S is the quantity of street lights consumed by Shobber. The Mayor of their town considers street lights to be a public good and is charged with purchasing the optimal number of street lights from Boone’s Light Shop. Boone’s is willing to sell street lights for $150 per light.

a.     In what sense, if any, do street lights qualify as a public good? What is the relationship between Q_M, Q_R, and Q_S (i.e., greater than, less than or equal to) likely to be when the Mayor installs the lights? Why?

1.    The oil is produced by a single refinery (a monopolist) which is owned by an entrepreneur called Sluggo. The demand for oil which is produced in Sluggo's refinery is Q= 50-P. The cost function of the refinery is given as: C(Q)=8+4Q.

It is also known that there is a (constant) marginal external cost of 6$ per unit of oil production resulting from environmental damage associated with production.

(b)  Is the amount you 22 units to maximize profits socially desirable level of output? Why or why not?

(c)  If your answer to (b) is no, what is the socially desirable level of output?

(d)  If the government decides to use corrective tax to force Sluggo to produce the socially desirable level of output, how much will Sluggo's tax bill be?

(e)If the government chooses to subsidize Sluggo for each unit that he does not produce, how much subsidy should be given to Sluggo?