COMM 295 Assignment 1

# This regression line provides an estimate or

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This regression line provides an estimate or approximation of the demand curve. Some of the data points do not lie exactly on the estimated regression line. Does this mean that the estimated demand curve is incorrect that it does not show the true relationship between price and quantity demanded? Explain briefly. (Hint: Read the discussion of random error on page 50 of the textbook) (3 pts) c) Suppose that a producer of granola uses in-store discounts to estimate the demand for its product (bags of granola) as Q = 60 5p per week for every 100 customers. If this demand curve is accurate and the price falls from 10 to 8, what is the arc elasticity of demand for this price change? (4 pts) d) If Q = 60 5p, at what price is the point elasticity of demand equal to -1? (3 pts) e) If demand is given by Q = 60 5p and the granola producer was initially charging \$5 per package of granola, could the firm raise its revenue by lowering price to \$4 per package? Derive an algebraic expression showing the relationship between revenue and price and illustrate this relationship on a diagram with price on the horizontal axis. Would it make sense to use a linear regression to estimate the relationship between revenue and price? Explain briefly. (6 pts.)

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4 Question 3: Consumer Choice a) Connie has a monthly budget of \$20 that she allocates between avocados (A) and tomatoes (T). Suppose the price of avocados (P A ) is \$4/kg and that of tomatoes (P T ) is \$2/kg. a) Write the equation for her budget line. (2 pts) b) If Connie's utility function over these two goods is given by U(A,T) = 5A + 2T, draw a graph. (Put T on the horizontal axis and put A on the vertical axis.) Show the combination of A and T that maximizes her utility subject to her budget constraint. (Hint: A and T are perfect substitutes for Connie.) (4 pts) c) Now assume that there is a special promotion for tomatoes. If Connie buys 5 kgs of tomatoes at the regular price, she gets the next 2.5 kgs for free. Any additional tomatoes cost the usual price of \$2/kg. Draw her budget line under this new promotional scheme. (4 pts) d) Will this new promotion scheme change Connie's utility-maximizing bundle? Draw a diagram to show her new utility-maximizing bundle. (5 pts) e) Instead of linear indifference curves, Wei has indifference curves that exhibit a diminishing marginal rate of substitution. Use two diagrams to show that this promotion may or may not increase Wei’s consumption of tomatoes. (5 pts) Question 4: Production A large auto parts manufacturer has the following production function: 0.4 10 Q KL where K = units of capital and L = units of labor.
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