Microeconomics Answers

Suppose u = x1^1/2 x2^1/2 Initially we have p1 = p2 =1. but then p1 rises to 2. The consumer’s income is $40

a) . Solve for the optimal points both pre and post price change and show these point on a clear complete graph.

b) Define in words what the CV associated with this price change represents for this consumer. Using the method covered in class, solve for the CV associated with this price change for this consumer. Show this on a graph.

c) Define in words what the EV associated with this price change represents for this consumer. Solve for the EV associated with this price change for this consumer. Show this on a graph.

d) Which measure of welfare change is larger? Why?

1. utility function u = x1^1/3 x2^2/3. and income = $60.

a) Solve for MU, and MU2 and use these to determine the MRS. Now use the tangency condition MRS = -p1/p2 together with budget line to solve for the demand functions for x1 and x2 for this consumer.

b) Initially we have p1 = 2 and p2 = 1, but then p1 falls to 1. Use your demands to solve for points A and C (the optimal points pre and post price change). Show these points on a clear well-labelled graph

c) Now determine the Slutsky demand by computing the income that would make point A just affordable with the new prices. Plug this hypothetical income and the new prices into your demands to solve for point B, as done in class. Show both the hypothetical budget line and point B on either your graph in a) or a new graph. Show the substitution and income effects on your graph, and compute them.

d) Graphically, do the same analysis using the Hicks decomposition method ( show it on a graph). Show the income and substitution effects on your graph.

A supplier supplies 50 T-shirts when the price is R60 per t-shirt and 90 t-shirts when the price is R110 per t-shirt.

a). Determine the equation of the supply function as a function of q?

b). How many additional t-shirts are sopplied for each successive R1 increase in price?

c). How many t-shirts are sopplied when the price is R85?

d). What is the price when 120 t-shirts are sopplied?

 The following table shows the potential output combinations of oranges and jars of prickly pear jelly (from the flower of the prickly pear cactus) for Florida and Arizona. a) Compute the opportunity cost of oranges in Florida in terms of jars of prickly pear jelly. Do the same for prickly pear jelly in terms of oranges. b) Compute the opportunity cost of oranges in Arizona in terms of jars of prickly pear jelly. Do the same for prickly pear jelly in terms of oranges. c) Would it make sense for Florida to specialize in producing oranges and for Arizona to specialize in producing prickly pear jelly and then trade? Why or why not? Florida Arizona Oranges Prickly Pear Jelly Oranges Prickly Pear Jelly 0 10 0 500 50 8 20 400 100 6 40 300 150 4 60 200 200 2 80 100 250 0 100 0

1.      Which of the following statements is true?*

a.      To an economist, demand is different from quantity demanded.

b.      A demand schedule is the numerical tabulation of the law of demand.

c.      A demand curve is the graphical representation of the direct relationship between price and quantity demanded.

d.      a and b

e.      a, b, and c

9. The table below illustrates the interaction of demand and supply in the market for gasoline.

Supply and Demand Schedule of Gasoline

Price (cents) Quantity Demanded Quantity Supplied

1.00 800 500

1.20 700 550

1.40 600 600

1.60 550 640

1.80 500 680

2.00 460 700

2.20 420 720

Suppose the price of gasoline is $1.60 per gallon.  

a. Is the quantity demanded higher or lower than at the equilibrium price?  ___________

b. What about the quantity supplies?  ___________

c. Is there a shortage in the market?  ___________

d. If so, how much? ___________

Suppose two firms are the sole producers of widget in West Africa, and they are faced with a market demand function given as P = 40 - 20Q While Dally Limited is located in Nigeria, Joy Manufacturing operates from Ghana. The firms' total cost function is given as TC = 12 + Q

a.) Determine the output and profit for each firm under Cournot's assumptions. [3 marks] b.) To aid Joy Manufacturing increase its output to the Stackelberg leader's output level, the Ghanaian government plans to support the firm with subsidies. In monetary terms what should be the value of the subsidy that will make Joy Manufacturing the leading firm in the market? [3 marks]

c.) Assume the fims now operates under Stackelberg' s assumptions, with Joy Manufacturing as the leader, determine output and profit for each firm. [4 marks]

In a one-shot and simultaneous game, Perfume Shop (PS) and Fragrance Shop (FS) are engaged in an advertising war aimed at earning a larger profit from the sales of perfumes in the Onaapo Kingdom. If Perfume Shop advertise and FS advertises, both firms will earn a sum of 15 million cedis (¢ 15 M) in profits. If neither firm advertises, FS will make 12 million cedis (¢ 12 M) and PS will make 6 million cedis (¢ 6 M). However, if PS advertises and FS does not, PS will make 30 million (¢ 30M) and Fs will earn a sum of 9 million cedis (¢ 9 M) in profit. Also, if FS decides to advertise and PS fails to do same PS will earn a profit of 3 million cedis with FS making a profit of 9 million cedis.

i. Write the above game in normal form (2 marks)

ii. Does Perfume Shop "PS" has a dominant strategy ? Provide a comprehensive explanation for your answer. (4 marks)

iii. Does the Fragrance Shop "FS" has a dominant strategy ? Explain your answer in detail. (4 marks)

c.) Suppose a monopoly producer is also a monopsonist in the labour market. Demand for the output is P=100 - Q. The production function is Q= L, and the labour supply curve is w= 10 + L. How much labour does the firm hire? What wage is paid? [10 marks]

d.) Suppose the labour market is competitive, the supply curve of labour is upward sloping and the amount of capital is fixed. If the output market changes from a competitive market to a monopoly, what is the effect on its demand for labour? Explain briefly (in not more than 50 words). [7 marks]

a.) EASTEK Co. operates in a competitive market. Its production function is q=L (to the power alpha) * K (to the power beta). The exponents alpha and beta are both less than 1. If the firm's capital is fixed, and it takes the wage and price as given, what is the firm's short-run demand for labour ? [13 marks]

b.) Pipi Co Ltd. operates in a competitive market. Its marginal product of labour is 1 over L (1÷L), and it takes the wage and prices as given. Derive the firm's short-run demand for labour as a function of "w" and "p".

How much labour will the firm hire if w = 2 and p = 10? [10 marks]