Question

1. Kabralium. Kabralium is a rare mineral used in the production of lightweight aircraft parts. The only existing Kabralium mines are located in Kabralstan. There are many small miners in Kabralstan and they all behave as price takers. The market supply curve has remained constant from 2000-2019, with one exception: in 2016 there was a natural disaster in Kabralstan which put many mines out of business for several months. Normal conditions were restored before the end of 2016, so 2016 is the only year when supply was affected. The demand curve has shifted (to the right) over the years, with one exception: the demand curve in 2016 was the same as the demand curve in 2015. (a) Plot the values of price and output in the usual way (i.e., with price on the vertical axis). Try to plot the values as accurately as possible. (b) Assuming that the demand curve is linear and that its slope is constant over time, estimate the slope of the demand curve. (Hint: use the data for 2015 and 2016 and the fact that demand was the same in 2015 and 2016.)

Table 1 Kabralium Year Price Quantity (millions of tones) (S per tone) 2010 8.5 91 2011 14.2 190 2012 16.3 198 2013 18.2 207 249 2014 16.8 2015 22.1 309 2016 34.3 275 2017 35.1 354 33.6 402 2018 2019 434 41.2

(a) Plot the values of price and output in the usual way (i.e., with price on the vertical axis). Try to plot the values as accurately as possible.

(b) Assuming that the demand curve is linear and that its slope is constant over time, estimate the slope of the demand curve. (Hint: use the data for 2015 and 2016 and the fact that demand was the same in 2015 and 2016.)

(c) Based on your estimate of the slope of the demand curve, derive the expression for the demand in year 2016 (and 2015), that is, find the values of a and b such that the demand is given by q = a − b p.

(d) Assuming that the supply curve is linear, estimate its equation (for a normal year, that is, not for 2016) based on the available data and on the information above. (Hint: draw a line through the points and estimate the values of the intercept and slope. Note: there is not precise, exact answer to this question, all you’re asked to do is to provide an estimate.)

(e) Experts predict that the 2020 demand curve for Kabralium will shift to the left by 40 units with respect to 2019 (that is, for a given price, quantity demanded is 40 units lower). Assuming that the slope of the demand curve remains the same as in previous years, estimate the equilibrium values of p and q in year 2020.

Answer 1

(a.) supply curve is given by =>>   p = 0.0954 q - 1.8045

{ PLOT THE DATA IN EXCEL and GETTING THE RESULTS}

supply curve y = 0.0954x - 1.8045 PRICE 50 100 150 200 250 QUANTITY 300 350 400 450 500

(b.) demand curve is given by =>> p = - 0.3588 x + 132.98

{ use the data for 2015 and 2016 }

demand curve PRICE y = -0.3588x + 132.98 270 275 280 285 295 300 305 310 315 290 QUANTITY

Price = -0.35 88 x Quantity + 132.98 . Quantity = -1 Price – 132-98) 0.3588 = -2.787 Price + 370 624 Demand - 9= 220. a curve .9 - 370:624 - 271874 ... Sa= 370.6242 b = 2.287 @ already solved in part ① p= 0.0954 q- 1.80 45 →.. q = I IP + 1. 80 45) 0.0954 10.482 p + 18.915 Supply Cuove

o on (2019 p= 41.2 - 9 = 370.620 - 2.787 xp - 370.624 - 2.787 *( 41-2) a2a5 = 256 -: It is given that in 2020, q- 92019 – 40 = 256 - 40 = 216 9202. = 216

P = -0.3588x (236) +132.98 I Bozo = $55.5