49:I[79858,["1216","static/chunks/eeac573e-cfb1e84259e7dde2.js","4649","static/chunks/4649-d659720c90d9ee35.js","6404","static/chunks/6404-6ef05b8bff2887b0.js","4797","static/chunks/4797-e81dc81e0c1c1336.js","2972","static/chunks/2972-ab992f8c79eda392.js","4296","static/chunks/4296-8f39ea5654a4f1ab.js","4235","static/chunks/4235-6fd3b88ee1c357a0.js","960","static/chunks/960-4945c17e7bdffd04.js","866","static/chunks/866-36e9a2593ae60457.js","6501","static/chunks/app/%5BsubjectLabel%5D/problems/%5BproblemHash%5D/page-756d64521be57e67.js"],"ProblemPageMemo"] 4a:T4c3,

P_d = a, P_s = cQ

При введении налога в долях от цены потребителя

P_s = \frac{cQ}{1 - t} = P_d = a \Rightarrow Q_e = \frac{a(1 - t)}{c}

T_1 = tP_dQ_e = \frac{a^2t(1 - t)}{c}

При введении налога в долях от цены производителя

P_s = (1 + t)cQ = P_d = a \Rightarrow Q_e = \frac{a}{c(1 + t)}

T_2 = \frac{tP_dQ_e}{1 + t} = \frac{a^2t}{c(1 + t)^2}

Осталось решить уравнение T_1 = T_2. Не забудем, что T > 0 \Rightarrow t > 0.

\frac{a^2t(1 - t)}{c} = \frac{a^2t}{c(1 + t)^2}

(1 - t)(1 + t)^2 =

t^2 + t - 1 = 0

t = \frac{\sqrt{5} - 1}{2} \approx 61,8\%

Ответ:

61,8%.