Answer to Question #215747 in Microeconomics for aghan

Question

A Monopolist producing and supplying cooking gas to Mombasa city faces the demand function. Q = 8800 – 20P. Its cost function is given by TC = 20Q + 0.05Q². 

i. Determine the quantity of cooking gas she will produce and the price she will charge to maximize profits and determine her profit.  

ii. Explain how her profits she will affected if regulators forced her to operate like a perfectly competitive firm.  

iii. Illustrate and compute deadweight loss and lost consumer surplus associated with her Monopoly operations. 

b. Based on any community project of your choice, use indifference curves and the budget concept to illustrate your understanding of consumer equilibrium

Answer 1

(i). A profit maximizing monopolist produces output at a point where marginal revenue (MR) equals marginal cost (MC).

$Q=800-20P\\P=\frac{8800-Q\\P}{20}\\P=440-0.05Q\\TR=Price \times Quantity\\TR=(400-0.05Q)Q\\TR=440Q-0.05Q^2\\MR=\frac{dTR}{dQ}=440-0.1Q\\Given \space TC=200Q-0.05Q^2\\MC=\frac{dTC}{dQ}=20 =0.1Q$

$MR=MC\\440-0.1Q=20+0.1Q\\440-20=0.1Q+0.1Q\\420=0.2Q\\Q=2100\\P=440-0.05(2100 0\\P=335$

$Profit=P×Q−AC×Q\\Profit=(P−AC)Q\\Profit=(335−20−0.1Q)Q\\Profit=315Q−0.1Q^2\\Profit=315(2100)−0.1(2100)^2\\ Profit=220500$

 the profit-maximizing quantity is 2100 and the price is $335 and the profit is 220500.

(ii) If regulator force to operation in perfect competition, the profit maximizing condition will be;

 $P=MC\\440-0.05Q=20+0.1Q\\440-20=0.1Q+0.05\\420=0.15Q\\Q=2800\\P=440-0.05(2800)\\P=300$

the price will fall to 300 and quantity will rise to 2800.

(iii). As per the above equations, the graph is drawn below:

Deadweight loss =area CEF

$\frac{ 1}{2} × (2800 – 2100) × (335-300)\\ \frac{ 1}{2} × 700 \times 35\\=12250\\$

Lost consumer surplus = area BCDE + area CEF

Area BCDE$=2100\times(335-300)=73500$

Lost consumer surplus =73500+12250=85750

                            

b)

A budget line shows combinations of two goods a consumer is able to consume, given a budget constraint while indifference curve shows combinations of the two goods yielding equal satisfaction. The consumer then chooses a combination of two goods at which an indifference curve is tangent to the budget line to maximize utility.Consumer's Equilibrium  is a state where a consumer spends given income purchasing one or more commodities to achieve maximum satisfaction.