Reference no: EM133124597
1. An industry of price-taking profit-maximising firms in perfect competition all produce using the same technology, and each has a total cost function given by: TC = 2q³ - 4q² + 3q
Where TC is measured in thousands of pounds per week, and q is measured in thousands of units per week. Then:
a) If the market price of output is p = £4.5 what is each firm's output and profit (or loss)?
b) If the market price of output is p = £11 what is each firm's output and profit (or loss)?
c) Show that each firm's long-run output is 1000 unit per week (i.e. 1 thousands of units per week).
d) What is the price of output when the industry is in equilibrium?
e) if the market demand is given by P = 11 - 0.01Q, where Q is the industry output in thousands of units per week, what is the industry's equilibrium output and how many firms are in the industry in equilibrium?
f) If the market demand shifts to P = 12 - 0.01Q, what is the industry's equilibrium output and how many firms are in the industry in the new equilibrium?
2. A firm called Shanghai Housing Limited has won a tender to build housing units within the X city council. As part of its initial planning, it found out that the demand and supply functions for houses in X city are given by the following:
Ps = θ + βQs and Qd= α - Pd
a) Represent the above functions on a suitable graph, properly labeling all the axes and curves.
b) Find the equilibrium values of quantity and price.
c) In order to increase housing units, X local council is thinking to offer a subsidy of £k per housing unit. Discuss, using post-subsidy expressions, the possible effects on equilibrium house prices and quantities if this decision is implemented.
d) Write expressions for the price elasticities of demand and supply of housing after the granting of the subsidy.
e) Write appropriate expression showing the projected total expenditure of X county council that is related to the subsidy.
Information available to Shanghai Housing Limited also indicated that the total variable cost for such a project is given by: TVC(Q) = δQ2+ μQ
Where Q is quantity of housing units produced and δ and are positive constants. You also know that the total costs is approximated to be £λ if no housing units are produced.
f (i) Using appropriate equations, write the estimated housing profit function for this firm.
f (ii) Using your information from f(i) or otherwise, work out an expression for the number of housing quantity that will maximize profit.