3. Consider an economy divided into agricultural sector, A, and service sector, S. To produce one unit in sector A requires 1/6 units from A and ¼ units from S. To produce a unit of S requires ¼ units from A and 1/4 units from S. 4 1 4 Suppose final demands in each of the two sectors are 50 units. Let x and y denote total production in industries A and S respectively. What is the Leontief system for this economy?

5. There are N>1 firms. Each firm is a price taker. At price level p, the output of a firm is q =p– 1 The demand function for the total output (across N firms) is 5 -р, р 5 Firms can only produce a nonnegative quantity of goods, and p must be nonnegative. (a) Compute the equilibrium price and quantity such that the quantity demanded equals quantity supplied. 1 (b) How much do the equilibrium price and quantity increase if N is increased by 1?

5. Next Monday, Concrete Co need to supply concrete to four different building sites. They prefer to use plants 1 and 2 for the production and delivery of the concrete, because they are quite close to the sites, but find it necessary to use plant 3 to satisfy the rest of the demand. The table below shows supply and demand amounts in tonnes, and cost coefficients in $ per tonne. Cij Site 1 70 40 130 75 Plant 1 Plant 2 Plant 3 Demand Site 2 40 50 210 23 Site 3 20 30 80 19 Site 4 50 60 90 25 Supply 80 55 7 Concrete Co wish to minimise their total cost. Treat this as a primal LP problem. (a) Show that Concrete Co have balanced their transportation problem. (b) Use the Least Cost Method to find a basic feasible solution to this primal problem. Verify that you have the correct number of basic variables. [Hint: You should look at 13 first. Then 12 and 21 are both contenders, but it does not matter what order you choose them in.] (c) Use complementary slackness conditions to find a dual…

Consider the following model of a monopolistic form, where P is the sale price of the good, MC is marginal cost of producing the good and q is quantity produced (assumed equal to quantity sold) the firm has to sell all units of the good at the same price. p=10-2q MC=2+q If the firm produces 3 units, what total revenue will it receive? a. £4 b. £6 c. £12 d. £24