QUESTION FIVE a) Briefly explain the assumptions of perfect competition. (3 marks) b) There are 100 firms in an industry each of which has no influence in the price prevailing in the market. Each firm is faced by a similar cost function of the form; C=0.1Q_(i)^2+Q_(i)+10 The total market demand function is given by the function D=4000-400P . The government has proposed a t% increase in ad valorem tax in an attempt to reduce consumption. i. Determine the equilibrium price and quantity before the tax is imposed. (6 marks) ii. If the tax proposal is carried out, determine the equilibrium quantity and price combination assuming the ad valorem tax is equal to 80% (6 marks)

a) The assumptions of perfect competition are:1. Large number of buyers and sellers: There are a large number of firms and consumers in the market, and no single firm or consumer can influence the market price.2. Homogeneous products: All firms produce identical or homogeneous products, and consumers perceive them as perfect substitutes.3. Free entry and exit: Firms can freely enter or exit the market, and there are no barriers to entry or exit.4. Perfect information: Consumers and firms have perfect knowledge about the market, including prices, products, and production methods.5. Profit maximization: Firms aim to maximize their profits by choosing the optimal level of output and price.b) i. To determine the equilibrium price and quantity before the tax is imposed, we need to set the market demand function equal to the market supply function. The market supply function is obtained by setting the marginal cost equal to the market price. The marginal cost is the derivative of the cost function with respect to the quantity.Given the cost function , the marginal cost is . Setting equal to the market price, we have .Now, we can set the market demand function equal to the market supply function and solve for the equilibrium quantity . Substituting into the market supply function, we get the equilibrium price .Therefore, the equilibrium price is and the equilibrium quantity is before the tax is imposed.ii. If the tax proposal is carried out, the ad valorem tax will increase the cost of production for firms. The new cost function will be , where is the tax rate.The new marginal cost will be . Setting equal to the new market price, we have .Now, we can set the new market demand function equal to the new market supply function and solve for the new equilibrium quantity . Substituting into the new market supply function, we get the new equilibrium price .Therefore, the new equilibrium quantity is and the new equilibrium price is after the tax is imposed.