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A) Graphically and Mathematically, Show That in Short Runs Profit Maximization , Firm Price of Marginal Product Is Equal to Input

Вопрос

a) Graphically and mathematically, show that in short runs profit maximization , firm price of marginal product is equal to input price. (8mks) b) A monopolist faces the following markets with the following demand functions Q=b_(0)-dot (b)_(1)P Show mathematically and illustrate diagrammatically the slope of the MR is twice the slope of AR (6mks) c) Derive the relationship between marginal urility and marginal rate of substitution (6mks) d) Suppose utility function of a consumer is given by II=f(x_(1)x_(2))=x^2/3x_(2)^1/2 Trice of commodity X_(1) is Ksh 10 per unit and price of commodity X_(2) is Ksh 15 per unit.How many units of two commodities, will he buy given that his income is equal to Ksh 450 (10mks) ESTION TWO (20MKS) 1) Mathematically, derive the relationship between price elasticity and marginal revenue of a firm. (6mks) ii) A. monopolist has the following total cost function Q=10div 5Q if the price elasticity for his product is -2 find out what price he will fix for his product.

Решения

4.3 (286 Голоса)
Маргарита
Экспертная проверка
эксперт · Репетитор 3 лет

Ответ

a) In the short run, a firm maximizes profit by equating the price of the marginal product to the input price. Graphically, this is represented by the point where the marginal cost curve intersects the price line. Mathematically, this can be shown by setting the marginal cost equal to the price of the input.b) For a monopolist with the demand function , the slope of the MR curve is twice the slope of the AR curve. This can be shown mathematically by differentiating the demand function with respect to price to find the slope of the AR curve, and then multiplying it by -2 to find the slope of the MR curve. Diagrammatically, the MR curve will be steeper than the AR curve.c) The relationship between marginal utility and marginal rate of substitution can be derived from the indifference map. The marginal rate of substitution is the rate at which a consumer is willing to trade one good for another while maintaining the same level of satisfaction. The marginal utility is the additional satisfaction a consumer receives from consuming one more unit of a good. The relationship is given by the equation: .d) Given the utility function , the consumer's budget constraint can be set up as . Solving this equation for and will give the number of units of each commodity the consumer will buy.QUESTION TWO1) The relationship between price elasticity and marginal revenue can be derived from the formula for elasticity: . Rearranging this equation gives , which is the formula for marginal revenue.ii) Given the total cost function and the price elasticity of -2, the monopolist can find the price by setting the elasticity equal to the ratio of the percentage change in quantity to the percentage change in price. Solving this equation for price will give the price the monopolist will fix for his product.