Mathematics for Management -- Supplementary Electronic Materials

Consumer Willingness to Spend & Consumer's Surplus

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1. Let the consumers' demand function for a certain commodity be \(D(q) = 4(25 - q^2)\) GEL per unit. Find the total amount of money consumers are willing to spend to get \(3\) units of the commodity.

\( 209 \) GEL \( 264 \) GEL \( 297 \) GEL \( 312 \) GEL

2. The demand for a product, in GEL, is \(p = D(q) = 1200 - 0.2 x - 0.0001 x^2\). Find the consumer surplus when the sales level is \(500\).

\( 25733.33 \) \( 29536.66 \) \( 33333.33 \) \( 35666.66 \)

3. Find the consumer's surplus at \(q = 5\) for the demand function \(p = D(q) = 30 - 4q\).

\( 30 \) \( 40 \) \( 50 \) \( 60 \)

4. Suppose all other conditions stay fixed. Then, when price decreases, consumer surplus

increases remains constant decreases becomes negative

5. A tire manufacturer estimates that \(q\) (thousand) radial tires will be purchased (demanded) by wholesalers when the price is \(p = D(q) = -0.1 q^2 + 90\) GEL per tire, and the same number of tires will be supplied when the price is \(p = S(q) = 0.2 q^2 + q + 50\) GEL per tire. Determine, in thousands of GEL, the consumer's surplus CS and the producer's surplus PS, respectively, at the equilibrium price (rounded to two digits).

CS = \(66.67\), PS = \(243.33\). CS = \(243.33\), PS = \(66.67\). CS = \(866.67\), PS = \(556.67 \) CS = \(556.67\), PS = \(866.67\).

6. The supply function for \(q\) casks of wine is given (in GEL) by \(p = S(q) = q^2 + 10 q\) and the demand function function is given (in GEL) by \(p = D(q) = 900 - 2x - x^2\). Determine, in GEL, the consumer's surplus CS and the producer's surplus PS, respectively, at the equilibrium price.

CS = \(3471\), PS = \(2284\) CS = \(2284\), PS = \(3471\) CS = \(6450\), PS = \(3375\) CS = \(3375\), PS = \(6450\)

7. Given the demand function \(p = 35 - q^2\) and the supply function \(p = 3 + q^2\) find the producer's surplus assuming pure competition.

\( 19 \) \( \frac{65}{3 \) \( 37 \) \( \frac{128}{3} \)

8. Suppose the demand for a product is given by \(p = D(q) = -0.8 q + 150\), in GEL, and the supply for the same product is given by \(p = S(q) = 5.2 q\), in GEL. Determine, in GEL, the consumer's surplus CS and the producer's surplus PS, respectively, at the equilibrium price.

CS = \(320\), PS = \(570 \) CS = \(570\), PS = \(320\) CS = \(625\), PS = \(250\) CS = \(250\), PS = \(625\)

9. Assume the demand function is \(p = D(q) = 196 - x^2\) and the supply function \(p = S(q) = x^2 + 4x + 126\). Determine the consumer's surplus CS and the producer's surplus PS, respectively, at the equilibrium price.

CS = \(938.33\), PS = \(721.66 \) CS = \(721.66\), PS = \(938.33 \) CS = \(133.33\), PS = \(83.33 \) CS = \(83.33\), PS = \(133.33\)

10. Suppose \(p = D(q) = \frac{196}{\sqrt{q}}\) is the price, in GEL per unit, that consumers are willing to pay for \(q\) units of an item, and \(p = S(q) = \sqrt{q}\) is the price, in GEL per unit, that producers are willing to accept for \(q\) units. Determine, in GEL, the consumer's surplus CS and the producer's surplus PS, respectively, at the equilibrium price.

CS = \(2744\), PS = \(914.66 \) CS = \(914.66\), PS = \(2744 \) CS = \(3299.25\), PS = \(1675.33\) CS = \(1675.33\), PS = \(3299.25\)

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Solution: 1b; 2c; 3c; 4a; 5a; 6b; 7d; 8d; 9d; 10a

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.