Quantitative Methods for Economics

Here is the demand function for pizza: Q = 100 – 2Ppizza + Ppasta + 0.1Y Ppizza is the price of pizza, Ppasta is the price of pasta, and Y is income. Suppose that the price of pizza is $10, the price of pasta is $12 and income is $1,000. Calculate the following: a) Price elasticity of demand. 1 marks b) Income elasticity of demand; and determine if pizza is a normal or inferior good. 2 marks c) Cross-price elasticity of demand; and determine if pasta is a substitute or a compliment. 2 marks 2. Maximize this function: 2×2 – xy subject to this constraint: 12 = x + y 5 marks 3. A business sells computer hardware (H) and software (S). The hardware sells for $70 and the software sells for $50. The total cost of selling these two goods is represented by this equation: TC = H2 + HS + S2 Find the maximum profit for this business, and the values of hardware and software where this is achieved. 5 marks 4. Your company manufactures nuts (N) and bolts (B). Find the number of nuts and bolts that maximizes profit given the below profit function and constraint. What is the profit at this value? 5 marks Profit = N + 2NB Constraint: 5 = N + 2B