Statistics Solutions

(See Steps) Suppose the market for Star Fruit is a competitive market, that every consumer in the market has the same individual demand function: q^D=9-3p+p_papaya+2I

Question: Suppose the market for Star Fruit is a competitive market, that every consumer in the market has the same individual demand function:

\[{{q}^{D}}=9-3p+{{p}_{papaya}}+2I\]

And that every firm in the market has the same individual supply function:

\[{{q}^{S}}=1+\frac{2}{3}p-{{p}_{fertilizer}}-2{{p}_{water}}\]
  1. If there are 100 consumers and 150 producers in the market, find the market demand and supply functions.
  2. The price of papayas = $12 per bushel, I = $30 thousand (enter into function as 30), the price of fertilizer = $3 per liter, and the price of water = $4 per drum. Use the market supply and demand functions to solve for the equilibrium price and quantity of star fruit.
  3. Find the price elasticities of market supply and demand at the equilibrium.
  4. Is demand elastic or inelastic at the equilibrium price and quantity? What about supply?
  5. Is star fruit a normal good? Find the income elasticity of demand at current prices.
  6. Are papayas complements or substitutes?

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