Calculate the producer surplus and consumer surplus in the equilibrium and illustrate them in a graph.

The lumber market in Australia
Suppose the demand and the supply for lumber  used for construction in Australia are given by
QD =100 – 2P
QS = 1
2P
Assume also that the market is perfectly competitive.
2.1. Compute the equilibrium price P* and quantity Q *.
2.2. Plot on a graph: the demand curve, the supply curve, and the equilibrium price and quantity.
2.3: Calculate the price elasticity of demand and price elasticity of supply at the equilibrium price and quantity.
2.4. Calculate the producer surplus and consumer surplus in the equilibrium and illustrate them in a graph.
2.5. Now suppose a pandemic hits and the government introduces a Homebuilder Scheme, which provides up to a fixed amount of money towards building a home or renovating an existing one. As a result, there is an increase in construction projects. Use a demand and supply graph to explain how this affects the equilibrium price and quantity in the market.
2.6. A number of factors now affect the market at once. First, the price of oil rises, increasing transportation costs. Second, landowners who supply logs to sawmills decide to hold off on cutting trees in response to the market conditions described in 2.5. Use a demand and supply graph to explain how these two events affect the equilibrium price and quantity. Show changes relative to the equilibrium you
illustrated in 2.5.
2.7. Steel is a substitute for lumber in construction. Now suppose the price for steel rises. Use a graph of supply and demand to show what happens in equilibrium. Show changes relative to the original equilibrium you found in 2.1.
2.8. Now go back to the setup of 2.1 once more and suppose that instead of introducing the Homebuilder scheme, the government introduces a subsidy of s=5 per unit of lumber transacted in the market. Calculate the new equilibrium quantity and the price paid by consumers and received by producers.
2.9. Given the subsidy in 2.8, calculate and illustrate in a graph the consumer surplus, producer surplus and subsidy expenditure.
2.10. Calculate the deadweight loss caused by the subsidy in 2.8 and illustrate it in a graph.
2.11. Who benefits more from the subsidy, consumers or producers? Why?

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