4. Consider a market where the supply function exhibits unitary elasticity: (25 2 Bi), where B 3} 0 is a parameter. The demand function is linear: Qd = a hp, where a: > 0 and b :> [I are parameters. (1.) Show that for any value of B 3} 0 the supply elasticity is: in fact, unitary (show that n = 1). (11.) we have an estimate of the demand elasticity E = 2 at a given equilibrium price p = 4 and quantity.r Q = 8. 'What are the values of the demand parameters a and b? (iii.) Given the information in part (ii.), what is the value of B? . Consider the equilibrium outlined in question 4, where we know the demand and supply elasticities local to the observed equilibrium: 5 = 2 and n = 1 at p = 4 and Q = 8. (i.) Show that the incidence of a small! specic tax on consumers is 33.300 (show that nip/alt = 1/3). (ii.) What if the tax were large (say t = 3) would the incidence of the tax on con sumers (Ago/At) change relative to a small tax? If so in which direction (larger or smaller)? (iii.) For the same situation what if the demand function took on the following nonlinear form: (2.1 = 16 0.5132. [s the demand elasticity still 2 for the tax free equilibrium where p : 4 and Q : 8? Show for a. small tax that the incidence on consumers is still 33.3%. 'Would the incidence of a large tax (say i : 3) on consumers (An/At) change relative to a small tax? If so in which direction (larger or smaller)? Hint: The nonlinear nature of the demand function makes solving for p and Q a bit cumbersome. [f you tr}r to solve explicitly for the incidence on consumers of a large tax (say t : 3) you will have a quadratic form for the price: (1102 +3p+ \"y = 0. where or, 13. and \"y are simply coefcients (numbers). You can solve for :9 using the quadratic equation where you choose the correct root such that the price is positive. Then you can plug the price into the demand function to get. the quantity