Demand for potatoes is given by Q d = 10? 9 P with Q measured in tons. The suppl

Question

Demand  for  potatoes  is  given  by Qd=  10?9PwithQ measured  in  tons.   The supply of potatoes is given by Qs=P^2 . (a)  Show the demand and supply functions on a graph, taking care to properly label both curves and both axes. (b)  Find the equilibrium price and quantity. (c)  Find the elasticity of demand and the elasticity of supply,  evaluated at the equilibrium price and quantity.  Is demand elastic, inelastic, or unit elastic?  Is supply elastic, inelastic, or unit elastic? (d)  Solve for the elasticity of demand as a function of the market price.  Draw this function for P [1/3, 2/3]. (e)  Suppose a (small) sales tax is imposed on potatoes.  Would the burden of the tax fall mostly on consumers, mostly on producers, approximately equally, or is it impossible to tell from the information above?  Explain Demand  for  potatoes  is  given  by Qd=  10?9PwithQ measured  in  tons.   The supply of potatoes is given by Qs=P^2 . (a)  Show the demand and supply functions on a graph, taking care to properly label both curves and both axes. (b)  Find the equilibrium price and quantity. (c)  Find the elasticity of demand and the elasticity of supply,  evaluated at the equilibrium price and quantity.  Is demand elastic, inelastic, or unit elastic?  Is supply elastic, inelastic, or unit elastic? (d)  Solve for the elasticity of demand as a function of the market price.  Draw this function for P [1/3, 2/3]. (e)  Suppose a (small) sales tax is imposed on potatoes.  Would the burden of the tax fall mostly on consumers, mostly on producers, approximately equally, or is it impossible to tell from the information above?  Explain

Explanation / Answer

The two equations are

Qd = 10 - 9 P. to calculate demand

Which would give Qd = 1. ( when P = 1)

Qd = -8. When P = 2

Plot these points on the graph with x axis as P and y axis as Q to get Demand curve.

For supply curve

Qs = P^2

Therefore, when P = 1 then Qs = 1

When P= 2 then Qs = 4

When P= 3 then Qs = 9

Plot these values on graph using P as x axis and Qs as y axis to get supply curve.

Equilibrium is given when Qs = Qd

Therefore, 10-9P = P^2

Solving for P, we get P = 1

Put P = 1 in equation for Qd

qd = 10-9= 1

Similarly Qs = 1

Elasticity is given by dQ/dP*(P/Q)

dQ/dP (for demand Qd) = -9

P and Qd at equilibrium are both = 1

Therefore demand elasticity is -9 (elastic)

Supply elasticity is dQs/dP = 3 (elastic)

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