Question

PART 1: Calculation Questions. Show all details of your math work. (While handwritten/scanned are accepted, you are encouraged to submit typed up answers.) (1) The early stage of a contagious virus outbreak has been reported in the city of Gotham. This city has the population of 20 million inhabitants. Currently only less than 0.01 percent of the population have contracted the virus. One easy yet unpopular methods to slow down the spread of this disease is using facemask. There is an established market for facemask with the following specifications: VP-5 Suppy: Qs = 0.2 Demand: Od = 20-P 0.3 Where l represents number of masks in million), and P isits price. Epidemiologists have discovered using mask has specific increasing external benefit to the society. The formula for this externality is MEB = 0.05Q^2 Given this information answer the following questions. Use all tools in your disposal to answer in details and clearly. 1. What percentage of the population is using the mask currently? Is it the socially efficient level? Explain. b. Should government be intervening? Give a recommendation on how government can step in. c. What are the costs and benefits of government intervention? d. In a thematic graph, show your work. (2) Imagine we have a society of two citizens, A and B, who can own and consume) two types of goods and services: private(X) and public(Y). Their utility functions are as follow: UA(XA,Y) = 2lnxa + InY UB(XB,Y) = Inxo + 2lny Where Xi is the level of the private good for citizen i and Y refers to the public good level. The production possibility frontier is: Y + X = 100, where X = Yxi. If the monetary endowment (wealth) of the citizens are 14 = $90,1 = $30 and the public good costs (MC) $5, answer the following questions: a. What are the market (collective) demand functions for X and Y? b. What is the optimal level of Public Good provision? c. What is the price of X and what are the Lindhal prices for the public good?

Answer 1

As per HomeworkLib policy I will answer the 4 subparts of the first question. Please post the second question again.

a. For equilibrium initially, Qs=Qd

(P-5)0.5/0.2= (20-P)0.5/0.3

(P-5)/0.04=(20-P)/0.09

0.09(P-5)=0.04(20-P)

0.13P=1.25

P=9.615

Therefore Qs=Qd= 10.742

And therefore the quantity of masks is 10.742 million and the percentage of population wearing it is 10.742/20*100=53.7096

It is the private equilibrium and does not take into account the external benefits and thus it is not the socially efficient level.

b) The government should be intervening to ensure the socially efficient level is being produced, one way this can be done by giving subsidies and therefore encouraging more production.

c) The costs of government benefits will be the government expenditure spent as part of the subsidies to be given, meanwhile the benefits will be the further increase in the external benefits as the socially efficient level is higher than the private equilibrium.

d) In the graph the following are plotted with Price and benefits on Y axis and Quantity on X axis

Private supply curve (Red x=5(y-5)^0.5)

Private demand curve Purple (can be expressed as both x=(1/0.3)(20-5)^0.5 or y=20-0.09x^2)

The point where they both intersect gives the private equilibrium (10.742,9.615)

Marginal external benefits (Green y=0.05x^2)

The Social benefit curve to find the socially optimal level (black) is given by vertically adding the demand curve and the marginal external benefits i.e. y=20-0.09x^2+0.05x^2

The point where it intersects the red supply curve(13.693,12.5) is the socially efficient level.

Therefore the government will have to give a subsidy of 12.5-9.615=2.885 per face mask to achieve the socially efficient level of output.

Hope it helps. Do ask for any clarifications required..

+ X X X x=567–530.5 or= oz (20 – y)0.5 y= 0.05x? y= 204 (0.09x2) y=20 – (0.09.x2)+0.05x2 X X 20 25 30 35 40 powered by desmos