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Man, I was completely demoralized by going through ME II section. Any aid regarding any of these questions would be great:
6. A monopolist has cost function c(y) = y so that its marginal cost is
constant at Re. 1 per unit. It faces the following demand curve
D (p) = 0 ; if p > 20
100/p ; if p 20.
Find the profit maximizing level of output if the government imposes a
per unit tax of Re. 1 per unit, and also the dead-weight loss from the
tax.
9. A monopolist sells two products, X and Y . There are three consumers
with asymmetric preferences. Each consumer buys either one unit of
a product or does not buy the product at all. The per-unit maximum
willingness to pay of the consumers is given in the table below.
Consumer No. X Y
1 4 0
2 3 3
3 0 4.
The monopolist who wants to maximize total payoffs has three alternative marketing strategies: (i) sell each commodity separately and
so charge a uniform unit price for each commodity separately (simple
monopoly pricing);(ii) offer the two commodities for sale only in a package comprising of one unit of each, and hence charge a price for the
whole bundle (pure bundling strategy), and (iii) offer each commodity separately as well as a package of both, that is, offer unit price for
each commodity as well as charge a bundle price (mixed bundling strategy). However, the monopolist cannot price discriminate between the
consumers. Given the above data, find out the monopolist’s optimal
strategy and the corresponding prices of the products.
14. Suppose that a monopolist operates in a domestic market facing a
demand curve p = 5 - (3/2)qh , where p is the domestic price and qh
is the quantity sold in the domestic market. This monopolist also has
the option of selling the product in the foreign market at a constant
price of 3. The monopolist has a cost function given by C(q) = q^2
,where q is the total quantity that the monopolist produces. Suppose,
that the monopolist is not allowed to sell more than 1/6 units of the
good in the foreign market. Now find out the amount the monopolist
sells in the domestic market and in the foreign market.
16. Consider two countries - a domestic country (with excess capacity and
unlimited supply of labour) and a benevolent foreign country. The
domestic country produces a single good at a fixed price of Re.1 per unit
and is in equilibrium initially (i.e., in year 0) with income at Rs. 100
and consumption, investment and savings at Rs. 50 each. Investment
expenditure is autonomous. Final expenditure in any year t shows up
as income in year t (say, Yt) , but consumption expenditure in year t
(say, Ct) is given by: Ct = 0.5Y(t-1)
The foreign country agrees to give a loan of Rs.100 to the domestic
country in year 1 at zero interest rate, but on conditions that it be
(i) used for investment only and (ii) repaid in full at the beginning of
the next year. The loan may be renewed every year, but on the same
conditions as above. Find the income, consumption, investment and
savings of the domestic country in year 1, year 2 and in final equilibrium
when the country takes the loan in year 1 only.
5. An economy produces two goods, food (F) and manufacturing (M).
Food is produced by the production function F = (LF)^1/2(T)^1/2
, where LF is the labour employed, T is the amount of land used and F is the
amount of food produced. Manufacturing is produced by the production function M = (LM)^1/2(K)^1/2
, where LM is the labour employed, K is the amount of capital used and M is the amount of manufacturing
production. Labour is perfectly mobile between the sectors (i.e. food
and manufacturing production) and the total amount of labour in this
economy is denoted by L. All the factors of production are fully employed. Land is owned by the landlords and capital is owned by the capitalists. You are also provided with the following data: K = 36; T = 49
, and L = 100. Also assume that the price of food and that of manufacturing are the same and is equal to unity.
(a) Find the equilibrium levels of labour employment in the food sector
and the manufacturing sector (i.e. LF and LM respectively)
(b)Next, we introduce a small change in the description of the economy
given above. Assume that everything remains the same except for the
fact that land is owned by none; land comes for free! How much labour
would now be employed in the food and the manufacturing sectors?
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