8. Explain (i) how the standard (neoclassical) downward sloping demand curve is derived from the indifference curve and the budget constraint, and (ii) the meaning of the downward sloping demand curve. [Note: For (ii), you must include the type of the good considered. Mathematical notations may be used, if they are clearly defined in words.] (ch. 5)

Q1

(29) The way that a firm combines inputs and factors of production in order to determine how much they can produce is represented by the firm’s Select one: a. profit function. b. cost function. c. production function.   (30) Which of the following statements is true about total utility and consumer behavior? Select one: a. It steadily decreases with each additional purchase. b. It increases at a steady rate with every additional purchase. c. It increases with each additional purchase, but at a decreasing rate.

minimum of 200 words please

1. An individual consumer's utility function and the budget constraint are described below. (ch. 5). U = xy s.t. m = Pxx+Pyy where, m = $100, Pz = $5, and py = $2. Note: 2 and y are the amount of x good and y good; m the amount of money, på the price of x good; Py the price of y good. (i) Find the marginal rate of substitution between x and y. (ii) Find the slope of the budget constraint (in value). [no need to draw the budget constraint.] (iii) Given the answers to (i) and (ii), find the optimal amount of each good, x* and y*. (iv) Find the level of utility obtained by this rational consumer. (v) Interpret the meaning of the answer you found in (iii) and (iv).

2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…