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1. Assume the market for pencils is perfectly competitive. The market supply and demand curves for pencils are given as follows:
Supply curve:
P = 4Q
Demand curve:
P = 264 – 40Q
The marginal cost curve for a typical pencil factory is:
MC = 12q
[1 mark] Determine the equilibrium price for pencils.
[1 mark] Determine the profit-maximizing equilibrium level of output for a pencil factory.
[1 mark] At the level of output determined above, is the factory making a profit, breaking even, or making a loss? Explain your answer.
[2 marks: Market output, number of firms] Assuming that all of the pencil factories are identical, how many pencil factories are producing pencils?
[1 mark] Determine the producer surplus the typical firm has under the conditions described above.
2. The demand and supply functions of the market for hardtack are described by
p = 10−2q
and
p = 3q.
[2 marks: plot; calculation] Plot the demand and supply functions and calculate the market’s equilibrium quantity and price (q⋆, p⋆).
[1 mark] What is the demand elasticity in equilibrium?
[1 mark] What is the consumer surplus in equilibrium?
[3 marks: plot; calculation; intuition] Now the pirate government imposes a per-unit tax of $5. Plot the new equilibrium with the tax and calculate the price paid by buyers along with the net price the sellers charge. Did the price paid by buyers or the price paid by sellers change more? Why?
[2 mark: calculation; labels] Calculate the new consumer surplus, the tax revenue, and the deadweight loss. Label each of these areas in a plot.
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