1. **Problem Statement:** Calculate the equilibrium prices and quantities for a two commodity market model. 2. **Step 1: Define demand and supply functions for each commodity.** _Let the commodities be X and Y. Assume linear demand and supply:_ Demand for X: $Q_{dX} = a - bP_X$ Supply for X: $Q_{sX} = c + dP_X$ Demand for Y: $Q_{dY} = e - fP_Y$ Supply for Y: $Q_{sY} = g + hP_Y$ (Note: Coefficients $a,b,c,d,e,f,g,h$ need to be provided or assumed.) 3. **Step 2: Equilibrium condition** At equilibrium, quantity demanded equals quantity supplied for both commodities: $$Q_{dX} = Q_{sX} \\ a - bP_X = c + dP_X$$ $$Q_{dY} = Q_{sY} \\ e - fP_Y = g + hP_Y$$ 4. **Step 3: Solve for equilibrium prices** For commodity X: $$a - c = bP_X + dP_X = (b+d)P_X \\ P_X^* = \frac{a - c}{b + d}$$ For commodity Y: $$e - g = fP_Y + hP_Y = (f + h)P_Y \\ P_Y^* = \frac{e - g}{f + h}$$ 5. **Step 4: Compute equilibrium quantities by substituting back:** For X: $$Q_X^* = c + dP_X^* = c + d\frac{a - c}{b + d}$$ For Y: $$Q_Y^* = g + hP_Y^* = g + h\frac{e - g}{f + h}$$ --- 6. **Part b: Four limitations of the theory of price elasticity of demand:** 1. The theory assumes ceteris paribus - other factors remain constant, which rarely holds true in reality. 2. Elasticity values can change over time; the theory may not accurately reflect dynamic consumer preferences. 3. It assumes availability of perfect information to consumers which is often unrealistic. 4. The theory does not account for the income effect or substitution effect explicitly. --- 7. **Part c: Comparison of equilibrium under perfect competition vs monopolistic competition:** - Under **perfect competition**, many firms produce identical products; equilibrium is at the point where marginal cost (MC) = marginal revenue (MR) = price (P), leading to allocative efficiency. - Under **monopolistic competition**, many firms produce differentiated products; each firm faces a downward-sloping demand curve. Equilibrium occurs where MR = MC but price exceeds marginal cost due to product differentiation. - **Diagrams:** - Perfect competition: horizontal demand curve intersects MC and MR at equilibrium price and quantity. - Monopolistic competition: downward sloping demand and MR curves with MC intersects MR at equilibrium quantity; price is above MC. --- This completes your question with detailed explanations.