You are not expected to absorb this sequence of

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You are not expected to absorb this sequence of equations immediately. They are here for two main reasons: for future reference, and to illustrate yet another way in which keeping track of the units can assist in understanding theoretical relations.
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2. Exercises 1. The demand curve in each period for Novoplacebo, the new miracle drug which doesn’t really do anything but is very attractively packaged, is given by the equation P = 60 – Q D , where P is in $/kg and Q D is in kg. (a) Calculate Total Revenue, in $, when P = $36/kg. (b) Rewrite the equation for this demand curve when: (i) P is measured in cents/kg and Q is in kg; (ii) P is in cents/kg and Q is in grams; (iii) P is in cents/gram and Q is in grams; (iv) P is in cents/gram and Q is in kg; (v) P is in $/pound and Q is in pounds (using the conversion factor 1 kg = 2.2 lbs.). (c) Calculate Total Revenue, in both $ and in cents, for each demand curve in (b) at the same position as in (a). 2. (a) The weekly supply curve for Doggy Yums Kanine Kibble is given by the equa- tion P = 4 + 0.26 Q S , where P is in $/kg and Q S is in kg/week. Assuming that there are 52 weeks in a year, give the supply equation when P is in $/kg and Q S is in kg/year. (b) The daily demand curve for Doggy Yums is given by the equation P = 40 – 4 Q D , where P is in $/kg and Q D is in kg/day. (i) Give the demand curve for February, 2003, with P in $/kg. (ii) Give the demand curve for the year 2003, with P in $/kg. 3. You are given the model in Example 8, except that now the units for the defined period are as follows: X is measured in tonnes, L in labour-hours, P X in $/tonne, and P L in $/labour-hour. (a) Give the correct units for the following: MFC L ; Total Revenue; MC; MP L ; MRP L ; and MR. (b) Identify which of the following equations are incorrect (definitionally or as prof- it-maximization conditions) for a firm that is a perfect competitor in the input market: (i) MRP L /MR = MP L ; (ii) P L /MP L = MRP L ; (iii) MP L = MFC L /MC; (iv) P L /MP L = MC; (v) MP L = MFC L / P L ; (vi) MRP L /MFC L = 1; (vii) P X MRP L /MP L . 4. In this period, the price of output P X is a constant $2.50/kg, the wage rate ( P L ) is a constant $40/labour-day, and the equation for the MP L curve is MP L = 40 – L , with MP L in kg/labour-day and L in labour-days. (a) What is the profit-maximizing number of labour-days to hire this period? (b) If P X and P L both double, how many labour-days should be hired? (c) If P X doubles with P L constant, what is the profit-maximizing level of L ? (d) If P L doubles with P X constant, how many labour-days should be hired? M4-8 MATH MODULE 4: USING ECONOMIC UNITS
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