Question

Supply-Demand analysis

Let the inverse market demand and supply curves for an arbitrary good be given by ?(??) = ? − ??? and ?(?? ) = ? + ??? , respectively, where ?? (conversely, ?? ) denotes quantity demanded (conversely, quantity supplied) and all lower-case Greek letters denote positive parameters such that ? > ??? > 0 and ? > ?

(a) Solve for the market equilibrium price (? ∗ ) and quantity (? ∗ ) and show this solution on a supply-demand graph.

(b) Suppose that the parameter ? (marginally) increases. What factor(s) might cause such a perturbation? Derive and sign the comparative statics terms ?? ∗ /?? and ?? ∗ /?? and amend the supply-demand graph from part (a) to illustrate the effect of an increase in ?.

(c) Calculate the own-price elasticity of market demand (??) at the equilibrium found in part (a).

(d) Determine how a (marginal) increase in ? effects the elasticity derived in part (c), i.e., derive and sign the expression ???/??.

(e) Suppose you estimate the following values for the model’s parameters: ? = 10, ? = 1, ? = 2, ? = 3. Determine the corresponding equilibrium values for the market price, quantity transacted, and own-price elasticity of market demand. Repeat this exercise now assuming that ? = 20 and all other estimated model parameters remain the same. How do your results comport with the comparative statics predictions derived in parts (b) and (d)?

Answer 1

Given : The inverse market demand and supply curves for an arbitrary good. We compute the equilibrium quantities and prices, and analyse the impact on them due to a change in .

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