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2. In a class of 120 students, everybody would take two hamburgers if the price were zero, and no one would buyhamburgers if the price were $4 or more. Assume that the class demand curve for hamburgers is linear and givea formula(a) describing quantity as a function of price (demand curve)(b) describing price as a function of quantity (this is sometimes called the inverse demand curve)Explain what the equation tells you for the demand for hamburgers when the price is $3.99.3. Total revenue is a function of quantity and can be computed byR= price×quantity. Show that the total revenuecurve corresponding to the demand curve found in Problem 2 is quadratic. At what value does its maximum orminimum occur?4. A firm’s average cost function is given by the quadraticy=x2-20x+ 120whereyis average cost in dollars per unit of output. The output price is $10 per unit.(a) Are there any output levels at which the firm just breaks even (i.e. price=average cost), if so find them.(b) Sketch the average cost function and justify your answer to part (a) graphically.(c) Over what range of prices does the firm make a loss at all output levels?5. The demand curve for a product is given byq= 120000-500p, and the supply curve is given byq= 1000pfor0≤q≤120000, where price is in dollars.(a) At a price of $100, what quantity are consumers willing to buy and what quantity are producers willing tosupply? Will the market push the prices up or down?(b) Find the equilibrium price and quantity. Does your answer to part (a) support the observation that marketforces tend to push prices closer the equilibrium. Sketch a graph label the axis and show your reasoning ona graph.(c) Suppose a tax of 1.5 dollars per item is imposed on the supplier. Find the new eqilibrium price and quantity.Support your answer graphically.6. Letfandgbe linear functions with equationsf(x) =m1x+b1andg(x) =m2x+b2.Isf◦galso a linearfunction. If so, what is the slope of its graph?
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